@danlun I was not suggesting that my code

(expand@@2)~(expr1);

was a means to simplify your expression. It was a side-comment only relevant to Markiyan's code.

@Christopher2222 "...powers of cos(x)...."

@nm Perhaps one can get a numeric solution from dsolve after converting to a differential equation (if the conversion is possible). Even for symbolic solution, dsolve can solve many nonlinear equations, and is much more powerful than intsolve.

@Markiyan Hirnyk wrote:

map(proc (c) options operator, arrow; expand(c) end proc, op(expr1)):
map(proc (c) options operator, arrow; expand(c) end proc, op(map(proc (c) options operator, arrow; expand(c) end proc, op(expr1))));

These steps are not valid transformations! The op causes a drop of all factors or terms other than the first. Indeed, your final answer is just the first term of the expansion of a subpart of the original expression. If you take out the ops, it is valid, and it is equivalent to simply

(expand@@2)~(expr1);

or

map(expand@@2, expr1);

I notice that problems 1 & 3 have been fixed today. I haven't had a chance to verify 2 & 4.

@Markiyan Hirnyk The source of the error is competely different in this question.

@Markiyan Hirnyk It is often easier to simply answer a Question than to look up a reference.

@litun 

restart:
Bstar := 3.60/(12.0+s)+14.00/(20.0+s):
Nrot := [-23.8279785337007-4.37234259951331*I,
      -23.8279785337007+4.37234259951331*I,
      -13.8480664440518,
      -12.2635728941426-2.65264168833545*I,
      -12.2635728941426+2.65264168833545*I,
      -4.24998018723859]:
rfw := unapply(mul(-Bstar*gm[i]+1, i = 1 .. 6), s);
for i to 6 do b[i] := rfw(Nrot[i]) end do;

Introduce an extra variable G as the sum of the others:
Sol:= {solve({seq(b[k], k= 1..6), G= add(gm[k], k= 1..6)},
 {seq(gm[k], k= 1..6), G})}:
map(x-> eval(G, x), Sol);


I can't think of a way to limit the number of solutions.

@stasya I think that you should use the definitions provided by Markiyan. Note that function has a very precise definition within the Maple language itself (which you can see at ?function ), and that this definition is somewhat counterintuitive. A procedure or routine is definitely not a function under this definition.

@Markiyan Hirnyk I agree with you 100% about what is the technically correct definition of function in Maple. However, I believe that the Asker was asking about how the terms are used in actual practice.

Mac Dude: Did you see this Answer? Did it help? Why no reply?

What output do you want in each of the cases? Would it help if you eliminated the constant term (constant wrt x0) before calling coeffs?

@Alejandro Jakubi I also have not received a single email since the update.

Markiyan: Have you received emails since the update, on Thursday I believe?

@Markiyan Hirnyk I would call it a command, but I don't think that that usage is universal. It's certainly not a function.

@Bendesarts Stop using evalm!

Matrix multiplication is done with . not with &*

Pi is spelled with capital P: Pi not pi.