Perhaps something like this?

> Zeroplus:= `#msub(mn("0"),mo("+"))`;
  Int(f(x), x=Zeroplus .. infinity);

And similarly, replacing plus with minus.

I can't really tell exactly what you want to do. Do you mean something like this?

with(plottools): with(plots):
P[0]:= implicitplot(x^2-y^2=1,x=-3..3,y=-3..3):
P[0];
for i from 1 to 5 do
  rotate(P[0],i*Pi/3,[0,0])
end do;

1) implicitplot is in the plots package. You either need

> with(implicitplot):

or

> plots[implicitplot](...);

2) You are using both [] and {} in the input. Those produce a list and a set respectively. You probably want to use parentheses ().

1) implicitplot is in the plots package. You either need

> with(implicitplot):

or

> plots[implicitplot](...);

2) You are using both [] and {} in the input. Those produce a list and a set respectively. You probably want to use parentheses ().

How many regions are produced by n lines in general position (no two parallel, no three coincident)? Note that the n'th line intersects each of the first n-1 lines in exactly one point, so splits in two exactly n of the regions created by the first n-1 lines. Thus the number of regions is R(n) = R(n-1) + n, with R(1) = 2, leading to

> simplify(rsolve({R(n)=R(n-1)+n, R(1)=2}, R(n)));

1/2*n+1/2*n^2+1 See also http://www.research.att.com/~njas/sequences/A000124

How many regions are produced by n lines in general position (no two parallel, no three coincident)? Note that the n'th line intersects each of the first n-1 lines in exactly one point, so splits in two exactly n of the regions created by the first n-1 lines. Thus the number of regions is R(n) = R(n-1) + n, with R(1) = 2, leading to

> simplify(rsolve({R(n)=R(n-1)+n, R(1)=2}, R(n)));

1/2*n+1/2*n^2+1 See also http://www.research.att.com/~njas/sequences/A000124

OK, that's clearer. You want to have a way to automatically generate a procedure with a given number of formal parameters. The basic pattern might be something like this, where the lower-level procedure q takes a list as argument. Note that _VARS and _BODY must be unassigned global variables.

> procgen:= proc(n) 
     local vars, x, i;
     vars := seq(cat(x,i),i=1..n);
     subs(_VARS = vars, _BODY = q([vars]), 
        proc(_VARS) _BODY end proc)
  end proc;

Then, for example:

> procgen(3);

proc (x1, x2, x3) q([x1, x2, x3]) end proc

OK, that's clearer. You want to have a way to automatically generate a procedure with a given number of formal parameters. The basic pattern might be something like this, where the lower-level procedure q takes a list as argument. Note that _VARS and _BODY must be unassigned global variables.

> procgen:= proc(n) 
     local vars, x, i;
     vars := seq(cat(x,i),i=1..n);
     subs(_VARS = vars, _BODY = q([vars]), 
        proc(_VARS) _BODY end proc)
  end proc;

Then, for example:

> procgen(3);

proc (x1, x2, x3) q([x1, x2, x3]) end proc

If L is a list of length n and t is a set of integers from 1 to n, applyop(`*`, t, L, -1) produces the list whose j'th element is -L[j] if j is in t, L[j] otherwise. In other words, you are applying the multiplication operator `*` with second argument -1 to those operands of L that are in t, while leaving the others alone. map(`<`, ..., 0) takes this list and transforms each element e to e < 0, so you now have a list of inequalities. Thus

 t ->  map(`<`, applyop(`*`,t,L,-1) , 0) 

is a function that takes the set t and returns the list of inequalities (+/-) L[i] < 0, using - for those i in t and + otherwise. Finally, with CPS a set of sets, the outer "map" applies this function to each member of CPS.

If L is a list of length n and t is a set of integers from 1 to n, applyop(`*`, t, L, -1) produces the list whose j'th element is -L[j] if j is in t, L[j] otherwise. In other words, you are applying the multiplication operator `*` with second argument -1 to those operands of L that are in t, while leaving the others alone. map(`<`, ..., 0) takes this list and transforms each element e to e < 0, so you now have a list of inequalities. Thus

 t ->  map(`<`, applyop(`*`,t,L,-1) , 0) 

is a function that takes the set t and returns the list of inequalities (+/-) L[i] < 0, using - for those i in t and + otherwise. Finally, with CPS a set of sets, the outer "map" applies this function to each member of CPS.

An indefinite-integral form of this, where g is the inverse function of f, and F an antiderivative of f, is int(g(y),y)=y*g(y)-F(g(y)) I don't know why Maple doesn't apply this formula to integrating a transcendental RootOf with respect to a linear parameter (it can integrate RootOf a polynomial). For example: int(RootOf(_Z*sin(_Z)-y),y) = y*RootOf(_Z*sin(_Z)-y)-sin(RootOf(_Z*sin(_Z)-y)) +RootOf(_Z*sin(_Z)-y)*cos(RootOf(_Z*sin(_Z)-y))

> combinat[powerset]({$1..5});

> combinat[powerset]({$1..5});

The reason you can't assign l after p is that after assigning p, one of the entries in l is 0=0 (which comes from k[1,2]=k[1,2]). You can't assign a value to 0 (even if that value is 0). I'm guessing that what you really want to do is assign those equations in l where the left side is something that can be assigned a value. So you might try

> assign(select(type, l, assignable=anything));

The reason you can't assign l after p is that after assigning p, one of the entries in l is 0=0 (which comes from k[1,2]=k[1,2]). You can't assign a value to 0 (even if that value is 0). I'm guessing that what you really want to do is assign those equations in l where the left side is something that can be assigned a value. So you might try

> assign(select(type, l, assignable=anything));