function Integrate(action)
format long

if nargin<1,
   action='initialize';
end;
    
  if strcmp(action,'initialize'),

figNumber=figure( ...
      'Name','Evaluate integrals using the Midpoint, Trapezoid, and Simpson''s rules', ...
      'units','normalized',...
      'Color', [.5 .5 .5], ...
      'pos',[.01 .07 .98 .86],...
       'NumberTitle','off', ...
      'Visible','on');
  axes('units','normalized',...
      'Visible','on',...
      'position',[.64 .30 .35 .44]);
  %general info for popup buttons----------------------------------------
  side=.05;
  ypos=.88;
  poplabelwidth=.09;
  poplabelheight=.09;
  
        %function popup----------------------------------------------------------
  
  
  labelStrFcn='Function';
   popupStr=str2mat('sin(x)',...
      'cos(x)','exp(x)','x^c','1/[d+sin(x)]','e^(-cx) * cos(x)','1/[1+(x-pi)^2]','e^x * cos(4x)');
  
 
   
    % Generic label information for popup button
   labelPos=[side-.03 ypos+.03 poplabelwidth+.03 poplabelheight-.03];
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',labelPos, ...
      'BackgroundColor',[.7 .7 .7], ...
      'HorizontalAlignment','center', ...
      'String',labelStrFcn);
    % Generic popup button information
   btnPos=[side-.03 ypos poplabelwidth+.03 poplabelheight-.03];
   popupHndlFcn=uicontrol( ...
      'Style','popup', ...
      'Units','normalized', ...
      'backgroundcolor','white',...      
      'Position',btnPos, ...
      'String',popupStr);
  %subdivisions popup----------------------------------------------------------
  
  
  labelStr='Subdivisions';
   popupStr=str2mat('1', '2',...
      '3',...
      '4','5','6','7');
  
 
   
    % Generic label information for popup button
   labelPos=[side+.11 ypos+.03 poplabelwidth poplabelheight-.03];
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',labelPos, ...
      'BackgroundColor',[.7 .7 .7], ...
      'HorizontalAlignment','center', ...
      'String',labelStr);
    % Generic popup button information
   btnPos=[side+.11 ypos poplabelwidth poplabelheight-.03];
   popupHndlSub=uicontrol( ...
      'Style','popup', ...
      'Units','normalized', ...
      'backgroundcolor','white',...
      'Position',btnPos, ...
      'String',popupStr);
    
  %left endpoint edit----------------------------------------------------------
  
  
  labelStrLeft='Left Endpt.=a';
  
    % Generic label information for popup button
   labelPos=[side+.22 ypos+.05 poplabelwidth poplabelheight-.05];
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',labelPos, ...
      'BackgroundColor',[.7 .7 .7], ...
      'HorizontalAlignment','center', ...
      'String',labelStrLeft);
    % Generic popup button information
   btnPos=[side+.22 ypos+.02 poplabelwidth poplabelheight-.06];
   popupHndlLeft=uicontrol( ...
      'Style','edit', ...
      'Units','normalized', ...
      'BackgroundColor','white',...
      'string','0',...
      'Position',btnPos);
   
   
   %right endpoint edit----------------------------------------------------------
  
  
  labelStrRight='Right Endpt.=b';
  
   
    % Generic label information for popup button
   labelPos=[side+.33 ypos+.05 poplabelwidth poplabelheight-.05];
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',labelPos, ...
      'BackgroundColor',[.7 .7 .7], ...
      'HorizontalAlignment','center', ...
      'String',labelStrRight);
    % Generic popup button information
   btnPos=[side+.33 ypos+.02 poplabelwidth poplabelheight-.06];
   popupHndlRight=uicontrol( ...
      'Style','edit', ...
      'Units','normalized', ...
      'backgroundcolor','white',...
      'Position',btnPos, ...
      'String','pi/2');
       
   %constant c edit----------------------------------------------------------
  
  
  labelStrLeft='Constant c';
  
    % Generic label information for popup button
   labelPos=[side+.22 ypos-.04 poplabelwidth poplabelheight-.05];
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',labelPos, ...
      'BackgroundColor',[.7 .7 .7], ...
      'HorizontalAlignment','Center', ...
      'String',labelStrLeft);
    % Generic popup button information
   btnPos=[side+.22 ypos-.07 poplabelwidth poplabelheight-.06];
   editHndlC=uicontrol( ...
      'Style','edit', ...
      'Units','normalized', ...
      'BackgroundColor','white',...
      'string','1',...
      'Position',btnPos);
   
   
   %constant d edit----------------------------------------------------------
  
  
  labelStrRight='Constant d';
  
   
    % Generic label information for popup button
   labelPos=[side+.33 ypos-.04 poplabelwidth poplabelheight-.05];
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',labelPos, ...
      'BackgroundColor',[.7 .7 .7], ...
      'HorizontalAlignment','center', ...
      'String',labelStrRight);
    % Generic popup button information
   btnPos=[side+.33 ypos-.07 poplabelwidth poplabelheight-.06];
   editHndlD=uicontrol( ...
      'Style','edit', ...
      'Units','normalized', ...
      'backgroundcolor','white',...
      'Position',btnPos, ...
      'String','2');
       
  
  %General info for push buttons----------------------------------
  pushleft=.51;
  pushbottom=.82;
  pushwidth=.09;
  pushheight=.08;
  
  
  
  
  
     % The simpson BUTTON-----------------------------------------------------------
  
    labelStr='Simpson''s';
    callbackStr='Integrate(''simp'')';
    cmdStr=str2mat( ...
        ' % Simpson''s Rule' ...
    );        
    
    % Generic  button information
    btnPos=[pushleft pushbottom-.2 pushwidth pushheight];
    uicontrol( ...
        'Style','pushbutton', ...
        'Units','normalized', ...
        'Position',btnPos, ...
        'String',labelStr, ...
        'Callback',callbackStr, ...
        'UserData',cmdStr);
       % The Trapezodial BUTTON-----------------------------------------------------------
  
    labelStr='Trapezoid';
    callbackStr='Integrate(''trap'')';
    cmdStr=str2mat( ...
        ' % Trapezoid Rule' ...
    );        
    
    % Generic  button information
    btnPos=[pushleft pushbottom-.1 pushwidth pushheight];
    uicontrol( ...
        'Style','pushbutton', ...
        'Units','normalized', ...
        'Position',btnPos, ...
        'String',labelStr, ...
        'Callback',callbackStr, ...
        'UserData',cmdStr);
    % The Midpoint BUTTON-----------------------------------------------------------
  
    labelStr='Midpoint';
    callbackStr='Integrate(''midp'')';
    cmdStr=str2mat( ...
        ' % Midpoint Rule' ...
    );        
    
    % Generic  button information
    btnPos=[pushleft pushbottom pushwidth pushheight];
    uicontrol( ...
        'Style','pushbutton', ...
        'Units','normalized', ...
        'Position',btnPos, ...
        'String',labelStr, ...
        'Callback',callbackStr, ...
        'UserData',cmdStr);
    
    %output fields ---------------------------
    left=0;
    bottom=.18;
    width=.6;
    height=.42;
    textstr=str2mat(' ',' % This program determines integrals', ...
        ' % by various methods.');
    framepos=[left bottom width height];
    uicontrol( ...
        'Style','text', ...
        'Units','normalized', ...
        'HorizontalAlignment','center', ...
        'Position',framepos, ...
        'BackgroundColor',[0.7 0.7 0.7], ...
        'ForegroundColor',[0 0 0], ...
        'String','   Subdiv:                       Value:                                                             Error:                                          Ratio:            ');
     
    textHndl=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.07 bottom+.05 width-.405 height-.1], ...
        'Callback','simprule', ...
        'String',textstr);
     textHndl2=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.27 bottom+.05 width-.405 height-.1], ...
        'Callback','simprule', ...
        'String','');
    textHndl3=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.02 bottom+.05 width-.555 height-.1], ...
        'Callback','simprule', ...
        'String','');
    textHndl4=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.47 bottom+.05 width-.485 height-.1], ...
        'Callback','simprule', ...
        'String','');
        textHndl8=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[.8 .8 .8], ...
        'Position',[.18 .61 .15 .03], ...
        'Callback','simprule', ...
        'String','');
  %useless output controls for more results-----------------------------------
    textHndl5=uicontrol( ...
        'Style','text', ...
        'Visible','off',...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.47 bottom+.05 width-.485 height-.1], ...
        'Callback','simprule', ...
        'String','');
  textHndl6=uicontrol( ...
        'Style','text', ...
        'Visible','off',...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.47 bottom+.05 width-.485 height-.1], ...
        'Callback','simprule', ...
        'String','');
     textHndl7=uicontrol( ...
        'Style','text', ...
        'Visible','off',...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.47 bottom+.05 width-.485 height-.1], ...
        'Callback','simprule', ...
        'String','');
    %Help Button---------------------------------------  
labelStr='Help';
   callbackStr='integrationhelp';
    helpHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'position',[.82 .15 .15 .08], ...
      'string',labelStr, ...
      'call',callbackStr);
     %more results button------------------------------------
 labelStr='More Results';
   callbackstrmore='Integrate(''moreresults'')';
   moreHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'position',[.2 .07 .2 .05], ...
      'string',labelStr, ...
      'call',callbackstrmore);
  
    %Close Button---------------------------------------  
labelStr='Close';
   callbackStr='close(gcf)';
    closeHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'position',[.82 .05 .15 .08], ...
      'string',labelStr, ...
      'call',callbackStr);

  
   %-possible errors----------------------------------------
uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',[.65 .89 .32 .03] , ...
      'BackgroundColor',[1 1 1], ...
      'HorizontalAlignment','left', ...
      'String','To Avoid Errors:');
   
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',[.65 .86 .32 .03] , ...
      'BackgroundColor',[1 1 1], ...
      'HorizontalAlignment','left', ...
      'String','1) Verify Left Endpt. is not equal to Right Endpt.');
   
   uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',[.65 .83 .32 .03] , ...
      'BackgroundColor',[1 1 1], ...
      'HorizontalAlignment','left', ...
      'String','2) For function x^c, the interval [a,b] should not contain 0 if c < 0');
   
  %function definitions-----------------------------------
  leftfun=.05;
  topfun=.62;
  funwidth=.08;
  funheight=.08;
   
  
     uicontrol( ...
      'Style','text', ...
      'Units','normalized', ...
      'Position',[.05 .68 .37 .03] , ...
      'BackgroundColor',[1 1 1], ...
      'HorizontalAlignment','left', ...
      'String','  See Help for explanations of functions, constants, and errors.');
   
      
  
  %data that needs to pass into the next section-------------------- 

  
  
  hndlList=[textHndl textHndl2 textHndl3 popupHndlSub popupHndlLeft popupHndlRight popupHndlFcn textHndl4 editHndlC editHndlD helpHndl textHndl5 textHndl6 textHndl7 textHndl8];
   passPrmt.handle=hndlList;
   passPrmt.clmap=[];
   set(figNumber,'UserData',passPrmt);

elseif strcmp(action,'moreresults')
     figNumber=gcf;
passPrmt=get(figNumber, 'UserData');
hndlList=passPrmt.handle;
   textHndl3=hndlList(3);
   sub=get(textHndl3,'String');
   textHndl5=hndlList(12);
   integraldiff=get(textHndl5,'String');
   textHndl6=hndlList(13);
   integralratio=get(textHndl6,'String');
   textHndl7=hndlList(14);
   asymerror=get(textHndl7,'String');
   textHndl8=hndlList(15);
   rule=get(textHndl8,'String');
    moreresults(sub,integraldiff,integralratio,asymerror,rule);
    
else   %evaluates the integral---------------------------------------------------
  figNumber=gcf;
passPrmt=get(figNumber, 'UserData');
hndlList=passPrmt.handle;
   
    
    integraldiff=zeros(1,10);
    integralratio=zeros(1,10);
    asymerror=zeros(1,10);
    N=[1 2 3 4 5 6 7];
    P=[-2 -1 -1/2 0 1/2 1 2 3 4 5];
    F=char('sin','cos','exp','power','cosdiv','ecos','xminpi','ecos4');
    
   
   textHndl=hndlList(1);
   textHndl2=hndlList(2);
   textHndl3=hndlList(3);
   textHndl4=hndlList(8);
   textHndl5=hndlList(12);
   textHndl6=hndlList(13);
   textHndl7=hndlList(14);
   textHndl8=hndlList(15);
  
   popupHndlSub=hndlList(4);
   n=get(popupHndlSub,'Value');
   n=N(1,n);
   
   popupHndlLeft=hndlList(5);
   a=get(popupHndlLeft,'String');
   a=eval(a);
   
   popupHndlRight=hndlList(6);
   b=get(popupHndlRight,'String');
   b=eval(b);
 
   popupHndlFcn=hndlList(7);
   fcn=get(popupHndlFcn,'Value');
   fcn=deblank(F(fcn,:));

   
   editHndlC=hndlList(9);
   c=get(editHndlC,'String');
   c=eval(c);
   
   editHndlD=hndlList(10);
   d=get(editHndlD,'String');
   d=eval(d);
   
   if strcmp(action,'simp')    %output for simpsons rule-------------------------------
       [integral,error,sub,ratio,integraldiff,integralratio,asymerror]=simprule(fcn,a,b,n,c,d,integraldiff,integralratio,asymerror);
       set(textHndl8,'String','Simpson''s Rule');
   elseif strcmp(action,'trap')    %output for trapzoid rule----------------------------
       [integral,error,sub,ratio,integraldiff,integralratio,asymerror]=trap(fcn,a,b,n,c,d,integraldiff,integralratio,asymerror);
       set(textHndl8,'String','Trapezoid Rule');
   elseif strcmp(action,'midp')    %output for midpoint rule-------------------------------   
       [integral,error,sub,ratio,integraldiff,integralratio,asymerror]=midp(fcn,a,b,n,c,d,integraldiff,integralratio,asymerror);
       set(textHndl8,'String','Midpoint Rule');
   end
   if a < b
   t=a:.01:b;
   else
   t=b:.01:a;
   end
   hold off
   cla;
   xmin=min(a,b);
   xmax=max(a,b);
   axis([xmin xmax 0 4]);
   axis 'auto y';
   hold on
   
if strcmp(fcn,'power')
   y=feval(fcn,t,c);
   plot(t,y);
   powlegend=strcat('x^(',num2str(c),')');
   legend(texlabel(powlegend),0);
   
elseif strcmp(fcn,'cosdiv')
    y=feval(fcn,t,1,d);
    plot(t,y);
    legend(strcat('1/[',num2str(d),'+sin(x)]'),0);
elseif strcmp(fcn,'ecos')
    y=feval(fcn,t,c);
    plot(t,y);
    c=(-1)*c;
    ecosleg=strcat('e^(',num2str(c),'x) cos(x)');
    legend(texlabel(ecosleg),0);
else
   y=feval(fcn,t);
   plot(t,y);
      if strcmp(fcn,'sin')
          legend('sin x',0);
      elseif strcmp(fcn,'cos')
          legend('cos x',0);
      elseif strcmp(fcn,'exp')
          legend('e^x',0);
      elseif strcmp(fcn,'xminpi')
          legend('1 / [1+(x-\pi)^2]',0);
      elseif strcmp(fcn,'ecos4')
          legend('e^x cos(4x)',0);
          
      end
   
end


    
outputstr=str2mat(sprintf('%2.16f',integral(1)),sprintf('%2.16f',integral(2)),...
                  sprintf('%2.16f',integral(3)),sprintf('%2.16f',integral(4)),...
                  sprintf('%2.16f',integral(5)),sprintf('%2.16f',integral(6)),...
                  sprintf('%2.16f',integral(7)),sprintf('%2.16f',integral(8)),...        
                  sprintf('%2.16f',integral(9)),sprintf('%2.16f',integral(10)));
            
outputstr2=str2mat(sprintf('%2.16f',error(1)),sprintf('%2.16f',error(2)),...
                   sprintf('%2.16f',error(3)),sprintf('%2.16f',error(4)),...
                   sprintf('%2.16f',error(5)),sprintf('%2.16f',error(6)),...
                   sprintf('%2.16f',error(7)),sprintf('%2.16f',error(8)),...
                   sprintf('%2.16f',error(9)),sprintf('%2.16f',error(10)));
outputstr3=str2mat(sprintf('%4.0f',sub(1)),sprintf('%4.0f',sub(2)),...
                   sprintf('%4.0f',sub(3)),sprintf('%4.0f',sub(4)),...
                   sprintf('%4.0f',sub(5)),sprintf('%4.0f',sub(6)),...
                   sprintf('%4.0f',sub(7)),sprintf('%4.0f',sub(8)),...
                   sprintf('%4.0f',sub(9)),sprintf('%4.0f',sub(10)));               
outputstr4=str2mat([],sprintf('%1.8f',ratio(2)),...
                   sprintf('%1.8f',ratio(3)),sprintf('%1.8f',ratio(4)),...
                   sprintf('%1.8f',ratio(5)),sprintf('%1.8f',ratio(6)),...
                   sprintf('%1.8f',ratio(7)),sprintf('%1.8f',ratio(8)),...
                   sprintf('%1.8f',ratio(9)),sprintf('%1.8f',ratio(10)));               
  outputstr5=str2mat([],sprintf('%2.16f',integraldiff(2)),...
                  sprintf('%2.16f',integraldiff(3)),sprintf('%2.16f',integraldiff(4)),...
                  sprintf('%2.16f',integraldiff(5)),sprintf('%2.16f',integraldiff(6)),...
                  sprintf('%2.16f',integraldiff(7)),sprintf('%2.16f',integraldiff(8)),...        
                  sprintf('%2.16f',integraldiff(9)),sprintf('%2.16f',integraldiff(10)));
            
outputstr6=str2mat([],[],...
                   sprintf('%2.16f',integralratio(3)),sprintf('%2.16f',integralratio(4)),...
                   sprintf('%2.16f',integralratio(5)),sprintf('%2.16f',integralratio(6)),...
                   sprintf('%2.16f',integralratio(7)),sprintf('%2.16f',integralratio(8)),...
                   sprintf('%2.16f',integralratio(9)),sprintf('%2.16f',integralratio(10)));
              
outputstr7=str2mat(sprintf('%2.16f',asymerror(1)),sprintf('%2.16f',asymerror(2)),...
                   sprintf('%2.16f',asymerror(3)),sprintf('%2.16f',asymerror(4)),...
                   sprintf('%2.16f',asymerror(5)),sprintf('%2.16f',asymerror(6)),...
                   sprintf('%2.16f',asymerror(7)),sprintf('%2.16f',asymerror(8)),...
                   sprintf('%2.16f',asymerror(9)),sprintf('%2.16f',asymerror(10))); 
               
               
               
set(textHndl,'String',outputstr);
set(textHndl2,'String',outputstr2);
set(textHndl3,'String',outputstr3);
set(textHndl4,'String',outputstr4);
set(textHndl5,'String',outputstr5);
set(textHndl6,'String',outputstr6);
set(textHndl7,'String',outputstr7);
hndlList(3)=textHndl3;
hndlList(12)=textHndl5;
hndlList(13)=textHndl6;
hndlList(14)=textHndl7;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function integrationhelp

figNumber=figure( ...
      'Name','Help for Numerical Integration program', ...
      'units','normalized',...
      'Color', [1 1 1], ...
      'pos',[.4 .4 .5 .5],...
       'NumberTitle','off', ...
      'Visible','on');
  %function explanations-----------------------------
 left=.01;
 bottom=.8;
 width=.9;
height=.12;
pos = [left bottom width height];
string = 'Subdivisions = k*2^n, where k is the value of Subdiv. and n goes from 1 to 10.';
h = uicontrol('Style','Text','Units','normalized','BackgroundColor', [1 1 1],'Position',pos,'String',string);



  
pos = [left bottom-.15 width height];
string = {'Constant c is used in the functions 1/[d+sin(cx)] and e^(-cx) * cos(x).'};

h = uicontrol('Style','Text','Units','normalized','BackgroundColor', [1 1 1],'Position',pos,'String',string);

  
  pos = [left bottom-.3 width height];
  string = {'Constant d is used in the function 1/[d+sin(cx)]'};
h = uicontrol('Style','Text','Units','normalized','BackgroundColor', [1 1 1],'Position',pos,'String',string);


  
                
    pos = [left bottom-.45 width height];
  string = {'To execute the integration, select all the parameters and click on either Midpoint, Trapezoid, or Simpson''s '};  
h = uicontrol('Style','Text','Units','normalized','BackgroundColor', [1 1 1],'Position',pos,'String',string);


                
    pos = [left bottom-.74 .45 .05];
  string = {'Program by Rob O''Connell, 2001'};  
h = uicontrol('Style','Text','Units','normalized','Position',pos,'String',string);

  %Close Button---------------------------------------  
labelStr='Close';
   callbackStr='close(gcf)';
    closeHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'position',[.82 .05 .15 .08], ...
      'string',labelStr, ...
      'call',callbackStr);
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function moreresults(sub,integraldiff,integralratio,asymerror,rule)

figNumber=figure( ...
      'Name','More Results:', ...
      'units','normalized',...
      'Color', [.5 .5 .5], ...
      'pos',[.01 .4 .8 .4],...
       'NumberTitle','off', ...
      'Visible','on');
  
    %output fields ---------------------------
    left=.01;
    bottom=.15;
    width=.98;
    height=.75;
    textstr=str2mat(' ',' % This program determines integrals', ...
        ' % by various methods.');
    framepos=[left bottom width height];
    uicontrol( ...
        'Style','text', ...
        'Units','normalized', ...
        'HorizontalAlignment','center', ...
        'Position',framepos, ...
        'BackgroundColor',[0.7 0.7 0.7], ...
        'ForegroundColor',[0 0 0], ...
        'String','        Subdiv:    Difference Between Successive Values:              Ratio of the Differences:                                         Asymptotic Error:                            ');
     
    textHndl=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.1 bottom+.05 width-.7 height-.12], ...
        'Callback','simprule', ...
        'String',textstr);
     textHndl2=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.39 bottom+.05 width-.7 height-.12], ...
        'Callback','simprule', ...
        'String','');
    textHndl3=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.02 bottom+.05 width-.91 height-.12], ...
        'Callback','simprule', ...
        'String','');
    textHndl4=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[1 1 1], ...
        'Position',[left+.68 bottom+.05 width-.7 height-.12], ...
        'Callback','simprule', ...
        'String','');
      textHndl8=uicontrol( ...
        'Style','text', ...
        'HorizontalAlignment','center', ...
        'Units','normalized', ...
        'Max',10, ...
        'BackgroundColor',[.8 .8 .8], ...
        'Position',[.4 .91 .2 .06], ...
        'Callback','simprule', ...
        'String','');
  
  
  
    %Close Button---------------------------------------  
labelStr='Close Window';
   callbackStr='close(gcf)';
    closeHndl=uicontrol( ...
      'Style','push', ...
      'Units','normalized', ...
      'position',[.03 .05 .94 .08], ...
      'string',labelStr, ...
      'call',callbackStr);
  
  %Output----------------------------------------------------------------
set(textHndl3,'String',sub);
set(textHndl4,'String',asymerror);
set(textHndl,'String',integraldiff);
set(textHndl2,'String',integralratio);
set(textHndl8,'String',rule);              
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [integral,error,sub,ratio,integraldiff,integralratio,asymerror] = trap(fcn,a,b,n,c,d,integraldiff,integralratio,asymerror)
integral=zeros(1,10);
error=zeros(1,10);
sub=zeros(1,10);
ratio=zeros(1,10);
ratio(1)=1;
if strcmp(fcn,'power') %trap for powers----------------------------------------------- 
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sumend=(1/2)*(feval(fcn,a,c) +feval(fcn,b,c));
sum=0;
for i=2:1:subdiv
    sum=sum+feval(fcn,t(i),c);
end


integral(k)=h*(sumend + sum);

if c==-1
    if a==0
     differ=0; 
    else
     differ=log(abs(b))-log(abs(a));
    end

else
differ=(power(b,c+1))/(c+1)-(power(a,c+1))/(c+1);
end
sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
    end
end

end 
elseif strcmp(fcn,'cosdiv') %trap ----------------------------------------------- 
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
c=1;
sumend=(1/2)*(feval(fcn,a,c,d) +feval(fcn,b,c,d));
sum=0;
for i=2:1:subdiv
    sum=sum+feval(fcn,t(i),c,d);
end


integral(k)=h*(sumend + sum);



%-----------------------------------------------------------------------------
twopiinterval=2*(atan(((tan(.5*pi*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))-...
              2*(atan(((tan(.5*(-pi)*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)));
const=0;
tempb=b;

while abs(tempb) > abs(pi/c)
    tempb=sign(tempb)*(abs(tempb)-abs(2*pi/c));
    const=const+1;
end


differ=2*(atan(((tan(.5*tempb*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)));
   if b>0
     differ=differ+const*twopiinterval;         
 else
     differ=differ-const*twopiinterval;
 end
const=0;
tempa=a;

while abs(tempa) > abs(pi/c)
    tempa=sign(tempa)*(abs(tempa)-abs(2*pi/c));
    const=const+1;
end

if a>0
differ=differ-2*(atan(((tan(.5*tempa*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))-const*twopiinterval;
else
 differ=differ-2*(atan(((tan(.5*tempa*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))+const*twopiinterval;
end
 %--------------------------------------------------

sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
    end
end

end 
    
elseif strcmp(fcn,'ecos') %trap ----------------------------------------------- 
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sumend=(1/2)*(feval(fcn,a,c) +feval(fcn,b,c));
sum=0;
for i=2:1:subdiv
    sum=sum+feval(fcn,t(i),c);
end


integral(k)=h*(sumend + sum);


differ=-(exp(-(b*c))*c*cos(b) - exp(-(b*c))*sin(b) - c)/((c^2)+1)+...
       (exp(-(a*c))*c*cos(a) - exp(-(a*c))*sin(a) - c)/((c^2)+1);


sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
    end
end

end     
    
    
    
    
else %trap for sin, cos, exp xminpi ecos4---------------------------------------------    
    
    for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sumend=(1/2)*(feval(fcn,a) +feval(fcn,b));
sum=0;
for i=2:1:subdiv
    sum=sum+feval(fcn,t(i));
end


integral(k)=h*(sumend + sum);

if strcmp(fcn,'sin')
   differ = -cos(b) + cos(a);
elseif strcmp(fcn,'cos')
   differ = sin(b) - sin(a);
elseif strcmp(fcn,'exp')  
   differ = exp(b) - exp(a);  
elseif strcmp(fcn,'xminpi')
   differ = atan(b-pi) + atan(pi) -(atan(a-pi) + atan(pi));
elseif strcmp(fcn,'ecos4')
   differ = (1/17)*(exp(b)*cos(4*b)+4*exp(b)*sin(4*b)-1) - ...
            (1/17)*(exp(a)*cos(4*a)+4*exp(a)*sin(4*a)-1);   
end
sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end
end

%more results ---------------------------------------------------------------------------
integraldiff(2:10)=integral(2:10)-integral(1:9);
integralratio(3:10) = integraldiff(2:9)./integraldiff(3:10);

%asym error-------------------------------------------
  if strcmp(fcn,'sin')
      asymderiv=cos(b)-cos(a);
  elseif strcmp(fcn,'cos')
      asymderiv=sin(a)-sin(b);
  elseif strcmp(fcn,'exp')
      asymderiv=exp(b)-exp(a);
  elseif strcmp(fcn,'power')
      asymderiv=power(b,c-1)*(c)-power(a,c-1)*(c);
  elseif strcmp(fcn,'cosdiv')
      asymderiv=-(d+sin(c*b))^(-2)*(c*cos(c*b))+(d+sin(c*a))^(-2)*(c*cos(c*a));
  elseif strcmp(fcn,'ecos') 
      asymderiv=((-c)*exp((-c)*b)*cos(b)-exp((-c)*b)*sin(b))-((-c)*exp((-c)*a)*cos(a)-exp((-c)*a)*sin(a));
  elseif strcmp(fcn,'ecos4')
      asymderiv=(exp(b)*cos(4*b)-4*exp(b)*sin(4*b))-(exp(a)*cos(4*a)-4*exp(a)*sin(4*a));
  elseif strcmp(fcn,'xminpi')   
      asymderiv=((-1)*((1+b*b-2*b*pi+pi*pi)^(-2))*(2*b-2*pi))-((-1)*((1+a*a-2*a*pi+pi*pi)^(-2))*(2*a-2*pi));
  end
  
  for k=1:10
      subdiv=2^k*n;
      h=(b-a)/subdiv;
      asymerror(k)=-((h*h)/12)*asymderiv;
  end
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [integral,error,sub,ratio,integraldiff,integralratio,asymerror] = midp(fcn,a,b,n,c,d,integraldiff,integralratio,asymerror)
integral=zeros(1,10);
error=zeros(1,10);
sub=zeros(1,10);
ratio=zeros(1,10);


ratio(1)=1;
ratio(2)=1;
h=(b-a)/n;
if strcmp(fcn,'power') %midp for powers-----------------------------------------------  
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sum=0;
for i=1:1:subdiv
    sum=sum+feval(fcn,t(i)+(h/2),c);
end


integral(k)=h * sum;

if c==-1
    if a==0
     differ=0; 
    else
     differ=log(abs(b))-log(abs(a));
    end

else
differ=(power(b,c+1))/(c+1)-(power(a,c+1))/(c+1);
end
sub(k)=subdiv;

error(k) = differ - integral(k);

 if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end


elseif strcmp(fcn,'cosdiv') %midp for cosdiv-----------------------------------------------  
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sum=0;
c=1;
for i=1:1:subdiv
    sum=sum+feval(fcn,t(i)+(h/2),c,d);
end


integral(k)=h * sum;
%-----------------------------------------------------------------------------
twopiinterval=2*(atan(((tan(.5*pi*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))-...
              2*(atan(((tan(.5*(-pi)*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)));
const=0;
tempb=b;

while abs(tempb) > abs(pi/c)
    tempb=sign(tempb)*(abs(tempb)-(abs((2*pi)/c)));
    const=const+1;
end


differ=2*(atan(((tan(.5*tempb*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)));
   if b>0
     differ=differ+const*twopiinterval;         
 else
     differ=differ-const*twopiinterval;
 end
const=0;
tempa=a;

while abs(tempa) > abs(pi/c)
    tempa=sign(tempa)*(abs(tempa)-(abs((2*pi)/c)));
    const=const+1;
end

if a>0
differ=differ-2*(atan(((tan(.5*tempa*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))-const*twopiinterval;
else
 differ=differ-2*(atan(((tan(.5*tempa*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))+const*twopiinterval;
end
 %--------------------------------------------------



sub(k)=subdiv;

error(k) = differ - integral(k);

 if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end

elseif strcmp(fcn,'ecos') %midp for cosdiv-----------------------------------------------  
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sum=0;
for i=1:1:subdiv
    sum=sum+feval(fcn,t(i)+(h/2),c);
end


integral(k)=h * sum;



differ=-(exp(-(b*c))*c*cos(b) - exp(-(b*c))*sin(b) - c)/((c^2)+1)+...
       (exp(-(a*c))*c*cos(a) - exp(-(a*c))*sin(a) - c)/((c^2)+1);


sub(k)=subdiv;

error(k) = differ - integral(k);

 if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end




%midp for sin, cos, exp---------------------------------------------    
else
    
    
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sum=0;
for i=1:1:subdiv
    sum=sum+feval(fcn,t(i)+(h/2));
end


integral(k)=h * sum;

if strcmp(fcn,'sin')
   differ = -cos(b) + cos(a);
elseif strcmp(fcn,'cos')
   differ = sin(b) - sin(a);
elseif strcmp(fcn,'exp')  
   differ = exp(b) - exp(a);  
elseif strcmp(fcn,'xminpi')
   differ = atan(b-pi) + atan(pi) -(atan(a-pi) + atan(pi));
elseif strcmp(fcn,'ecos4')
   differ = (1/17)*(exp(b)*cos(4*b)+4*exp(b)*sin(4*b)-1) - ...
            (1/17)*(exp(a)*cos(4*a)+4*exp(a)*sin(4*a)-1);
end
sub(k)=subdiv;

error(k) = differ - integral(k);

if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end
end

%more results ---------------------------------------------------------------------------
integraldiff(2:10)=integral(2:10)-integral(1:9);
integralratio(3:10) = integraldiff(2:9)./integraldiff(3:10);

%asym error-------------------------------------------
  if strcmp(fcn,'sin')
      asymderiv=cos(b)-cos(a);
  elseif strcmp(fcn,'cos')
      asymderiv=sin(a)-sin(b);
  elseif strcmp(fcn,'exp')
      asymderiv=exp(b)-exp(a);
  elseif strcmp(fcn,'power')
      asymderiv=power(b,c-1)*(c)-power(a,c-1)*(c);
  elseif strcmp(fcn,'cosdiv')
      asymderiv=-(d+sin(c*b))^(-2)*(c*cos(c*b))+(d+sin(c*a))^(-2)*(c*cos(c*a));
  elseif strcmp(fcn,'ecos') 
      asymderiv=((-c)*exp((-c)*b)*cos(b)-exp((-c)*b)*sin(b))-((-c)*exp((-c)*a)*cos(a)-exp((-c)*a)*sin(a));
  elseif strcmp(fcn,'ecos4')
      asymderiv=(exp(b)*cos(4*b)-4*exp(b)*sin(4*b))-(exp(a)*cos(4*a)-4*exp(a)*sin(4*a));
  elseif strcmp(fcn,'xminpi')   
      asymderiv=((-1)*((1+b*b-2*b*pi+pi*pi)^(-2))*(2*b-2*pi))-((-1)*((1+a*a-2*a*pi+pi*pi)^(-2))*(2*a-2*pi));
  end
  
  for k=1:10
      subdiv=2^k*n;
      h=(b-a)/subdiv;
      asymerror(k)=((h*h)/24)*asymderiv;
  end
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [integral,error,sub,ratio,integraldiff,integralratio,asymerror] = simprule(fcn,a,b,n,c,d,integraldiff,integralratio,asymerror)
integral=zeros(1,10);
error=zeros(1,10);
sub=zeros(1,10);
ratio=zeros(1,10);
ratio(1)=1;
h=(b-a)/n;
if strcmp(fcn,'power') %for power function---------------------------------------
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sumend=feval(fcn,a,c) +feval(fcn,b,c);
sumodd=0;
for i=2:2:subdiv
    sumodd=sumodd+feval(fcn,t(i),c);
end
sumeven=0;
for i=3:2:subdiv-1;
    sumeven=sumeven + feval(fcn,t(i),c);
end

integral(k)=(h/3)*(sumend + 4*sumodd + 2*sumeven);

if c==-1
    if a==0
     differ=0; 
    else
     differ=log(abs(b))-log(abs(a));
    end

else
differ=(power(b,c+1))/(c+1)-(power(a,c+1))/(c+1);

end

sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end

elseif strcmp(fcn,'cosdiv')%for 1/(d + cos cx)------------------------------------
  for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
c=1;
t=a:h:b;
sumend=feval(fcn,a,c,d) +feval(fcn,b,c,d);
sumodd=0;
for i=2:2:subdiv
    sumodd=sumodd+feval(fcn,t(i),c,d);
end
sumeven=0;
for i=3:2:subdiv-1;
    sumeven=sumeven + feval(fcn,t(i),c,d);
end

integral(k)=(h/3)*(sumend + 4*sumodd + 2*sumeven);


%-----------------------------------------------------------------------------
twopiinterval=2*(atan(((tan(.5*pi*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))-...
              2*(atan(((tan(.5*(-pi)*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)));
const=0;
tempb=b;

while abs(tempb) > abs(pi/c)
    tempb=sign(tempb)*(abs(tempb)-abs(2*pi/c));
    const=const+1;
end


differ=2*(atan(((tan(.5*tempb*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)));
   if b>0
     differ=differ+const*twopiinterval;         
 else
     differ=differ-const*twopiinterval;
 end
const=0;
tempa=a;

while abs(tempa) > abs(pi/c)
    tempa=sign(tempa)*(abs(tempa)-abs(2*pi/c));
    const=const+1;
end

if a>0
differ=differ-2*(atan(((tan(.5*tempa*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))-const*twopiinterval;
else
 differ=differ-2*(atan(((tan(.5*tempa*c)*d)+1)/(sqrt(d^2-1)))-atan(1/(sqrt(d^2-1))))/(c*(sqrt(d^2-1)))+const*twopiinterval;
end
 %--------------------------------------------------
sub(k)=subdiv;
error(k) = differ - integral(k);
   if k>1
      if abs(error(k)) == 0
        ratio(k)=1;
      else
      ratio(k)=error(k-1)/error(k);
      end
   end
end
  
elseif strcmp(fcn,'ecos')%for ecos-------------------------------------------
    for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sumend=feval(fcn,a,c) +feval(fcn,b,c);
sumodd=0;
for i=2:2:subdiv
    sumodd=sumodd+feval(fcn,t(i),c);
end
sumeven=0;
for i=3:2:subdiv-1;
    sumeven=sumeven + feval(fcn,t(i),c);
end

integral(k)=(h/3)*(sumend + 4*sumodd + 2*sumeven);

differ=-(exp(-(b*c))*c*cos(b) - exp(-(b*c))*sin(b) - c)/((c^2)+1)+...
        (exp(-(a*c))*c*cos(a) - exp(-(a*c))*sin(a) - c)/((c^2)+1);


sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end
    
    
    
    
else  %for sin, cos, exp xminpi ecos4---------------------------------------------    
for k=1:10
subdiv=2^k*n;
h=(b-a)/subdiv;
t=a:h:b;
sumend=feval(fcn,a) +feval(fcn,b);
sumodd=0;
for i=2:2:subdiv
    sumodd=sumodd+feval(fcn,t(i));
end
sumeven=0;
for i=3:2:subdiv-1;
    sumeven=sumeven + feval(fcn,t(i));
end

integral(k)=(h/3)*(sumend + 4*sumodd + 2*sumeven);
if strcmp(fcn,'sin')
   differ = -cos(b) + cos(a);
elseif strcmp(fcn,'cos')
   differ = sin(b) - sin(a);
elseif strcmp(fcn,'exp')  
   differ = exp(b) - exp(a);  
elseif strcmp(fcn,'xminpi')
   differ = atan(b-pi) + atan(pi) -(atan(a-pi) + atan(pi));
elseif strcmp(fcn,'ecos4')
   differ = (1/17)*(exp(b)*cos(4*b)+4*exp(b)*sin(4*b)-1) - ...
            (1/17)*(exp(a)*cos(4*a)+4*exp(a)*sin(4*a)-1);
end
sub(k)=subdiv;
error(k) = differ - integral(k);
if k>1
    if abs(error(k)) == 0
        ratio(k)=1;
    else
    ratio(k)=error(k-1)/error(k);
end
end
end

end

%more results ---------------------------------------------------------------------------
integraldiff(2:10)=integral(2:10)-integral(1:9);
integralratio(3:10) = integraldiff(2:9)./integraldiff(3:10);

%asym error-------------------------------------------
  if strcmp(fcn,'sin')
      asymderiv=-cos(b)+cos(a);
  elseif strcmp(fcn,'cos')
      asymderiv=sin(b)-sin(a);
  elseif strcmp(fcn,'exp')
      asymderiv=exp(b)-exp(a);
  elseif strcmp(fcn,'power')
      asymderiv=power(b,c-3)*c*(c-1)*(c-2)-power(a,c-3)*c*(c-1)*(c-2);
  elseif strcmp(fcn,'cosdiv')
      asymderiv=-6/(d+sin(b))^4*cos(b)^3-6/(d+sin(b))^3*cos(b)*sin(b)+1/(d+sin(b))^2*cos(b)-...
               (-6/(d+sin(a))^4*cos(a)^3-6/(d+sin(a))^3*cos(a)*sin(a)+1/(d+sin(a))^2*cos(a));
  elseif strcmp(fcn,'ecos') 
      asymderiv=-c^3*exp(-c*b)*cos(b)-3*c^2*exp(-c*b)*sin(b)+3*c*exp(-c*b)*cos(b)+exp(-c*b)*sin(b)+...
                c^3*exp(-c*a)*cos(a)+3*c^2*exp(-c*a)*sin(a)-3*c*exp(-c*a)*cos(a)-exp(-c*a)*sin(a);
  elseif strcmp(fcn,'ecos4')
      asymderiv=-47*exp(b)*cos(4*b)+52*exp(b)*sin(4*b)+...
                 47*exp(a)*cos(4*a)+52*exp(a)*sin(4*a);
  elseif strcmp(fcn,'xminpi')   
      asymderiv=-6/(1+(b-pi)^2)^4*(2*b-2*pi)^3+12/(1+(b-pi)^2)^3*(2*b-2*pi)+...
                 6/(1+(a-pi)^2)^4*(2*a-2*pi)^3-12/(1+(a-pi)^2)^3*(2*a-2*pi);
  end
  
  for k=1:10
      subdiv=2^k*n;
      h=(b-a)/subdiv;
      asymerror(k)=-((h^4)/180)*asymderiv;
  end
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [value] = ecos(x,c)

value = exp(-(c.*x)).*cos(x);
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [value] = cosdiv(x,c,d)

value = 1./(d + sin(c.*x));
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [value] = ecos4(x)

value = exp(x).*cos(4.*x);
  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [value] = xminpi(x)

value = 1./(1+((x-pi).^2));