OK, thanks for the help so far.

I do have a follow-up question: What can one do about this bug?

OK, thanks for the help so far.

I do have a follow-up question: What can one do about this bug?

This does not work if one wants to integrate more complicated functions, say

int(x^2*f(x),x=0..1);

I have also tried using indexed variables, but maple does not like those:

g:=proc(j)
if j=0 then
  x[1]->int(x[1]*x[0],x[0]=0..1)
else
  x[j+1]->int(x[j+1]*g(j-1)(x[j]),x[j]=0..1)
fi:
end:

This is about what I meant by recursive definition with integrals.

This does not work if one wants to integrate more complicated functions, say

int(x^2*f(x),x=0..1);

I have also tried using indexed variables, but maple does not like those:

g:=proc(j)
if j=0 then
  x[1]->int(x[1]*x[0],x[0]=0..1)
else
  x[j+1]->int(x[j+1]*g(j-1)(x[j]),x[j]=0..1)
fi:
end:

This is about what I meant by recursive definition with integrals.

This does not answer my question. I still do not understand why my definition gives wrong results.

Why does

h:=z->z^2;

define an operator, but not

h:=z->f(2)(z);

even though maple tells me that f(2)(z) is z^2 ?

This does not answer my question. I still do not understand why my definition gives wrong results.

Why does

h:=z->z^2;

define an operator, but not

h:=z->f(2)(z);

even though maple tells me that f(2)(z) is z^2 ?