@Deltafee Please upload your worksheet so that I can diagnose the problem. Here's my doing of it:

Download NonlinearFit.mw

Your system is so large that I don't think that there's much hope for dsolve being able to handle it. The size of sys as measured by length({sys}) is over 2 Gig. That's so large that the length command itself takes several seconds to finish.

@acer How much of the computation of evalf(3/Pi, 1) is done in evalhf? Is it just the numeric evaluation of Pi?

@ecterrab My opinion is that it is an improvement---above and beyond the call of duty.

@Deltafee It should be

sol[1]:= Statistics:-NonlinearFit(f, xlist, ylist, x);

This is only a partial explanation: Since Digits is less than 16, the computation evalf(3/Pi, 1) is done in hardware double precision (evalhf mode). This makes it harder to see what's going on, because the debugger shows nothing. That being said, I consider the 0.9 result a bug.

@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.