Code:

`#cas`

simpsonint(g,a,b,n):=

BEGIN

local l,l1;

IF even(n) THEN

IF (type(g)==DOM_SYMBOLIC OR type(g)== DOM_FUNC)

THEN

l:=MAKELIST(X,X,a,b,(b-a)/n);

IF type(g)==DOM_SYMBOLIC THEN

g:=unapply(g,x);

END;

l:=apply(g,l);

l1:=MAKELIST(even(X)+1,X,1,n+1);

return (2*DOT(l,l1)-g(a)-g(b))*(b-a)/(3*n);

ELSE return ("f must be symbolic or function!");

END;

// return 0;

ELSE return "n must be even!";

END;

END;

#end

#cas

trapezregel(g,a,b,n):=

BEGIN

local l;

IF (type(g)==DOM_SYMBOLIC OR type(g)== DOM_FUNC)

THEN

l:=MAKELIST(X,X,a,b,(b-a)/n);

IF type(g)==DOM_SYMBOLIC THEN

g:=unapply(g,x);

END;

l:=apply(g,l);

return (2*ΣLIST(l)-g(a)-g(b))*(b-a)/(2*n);

ELSE return ("f must be symbolic or function!");

END;

END;

#end

#cas

rightsum(g,a,b,n):=

BEGIN

local l;

IF (type(g)==DOM_SYMBOLIC OR type(g)== DOM_FUNC)

THEN

l:=MAKELIST(X,X,a,b,(b-a)/n);

IF type(g)==DOM_SYMBOLIC THEN

g:=unapply(g,x);

END;

l:=apply(g,l);

return (ΣLIST(l)-g(a))*(b-a)/n;

ELSE return ("f must be symbolic or function!");

END;

END;

#end

#cas

leftsum(g,a,b,n):=

BEGIN

local l;

IF (type(g)==DOM_SYMBOLIC OR type(g)== DOM_FUNC)

THEN

l:=MAKELIST(X,X,a,b,(b-a)/n);

IF type(g)==DOM_SYMBOLIC THEN

g:=unapply(g,x);

END;

l:=apply(g,l);

return (ΣLIST(l)-g(b))*(b-a)/n;

ELSE return ("f must be symbolic or function!");

END;

END;

#end

EXPORT NumericIntegr()

BEGIN

local a,N,f,b;

N:=12; a:=1;b:=3;

f:='X^2';

if input(

{{f,[8],{20,70,0}},

{a,[0],{20,30,1}},

{b,[0],{20,30,2}},

{N,[0],{20,30,3}}},

"Enter Data",

{"f(X)=", "a= ", "b= ","N= "

},

{

"Enter the function, upper case X!",

"Enter the starting point",

"Enter the endpoint",

"Enter the amount of intervals"

},

{f,a,b,N}

)

then

f:=lower(string(f));

PRINT();

PRINT("Simpsonsumme: "+simpsonint(f,a,b,N));

PRINT("Trapezsumme: "+trapezregel(f,a,b,N));

PRINT("Rechtecklinks: "+leftsum(f,a,b,N));

PRINT("Rechteckrechts: "+rightsum(f,a,b,N));

return

end;

END;

after you run it once the cas-functions are shown in memory manager whilst the main program can be seen in toolbox user menu (concerning your other thread)