@Kitonum 
The highest class of Maple using, Yuri Nikolaevich!
(Maple17 works.)

A reminder of the turbulent inappropriate activity on the forum MaplePrimes
https://www.mapleprimes.com/posts/204297-Is-There-A-Way-To-Avoid-The-Consequences

@spalinowy 
and this is only one variable s. Listen to the first advice by Mariusz Iwaniuk.
( Do not mock your computer.)

@spalinowy 
You said that you are solving a system of 5 equations, right? Which variables do you want to find? Only s? In this case, I'm afraid you do not very well do what you need, and you were given a very correct answer.
If this is not the case, then please let us know in detail what the real situation is.

Will not say  that I understand the problem, but you can build a pyramid with the help of
(Не скажу, что понимаю задачу, но строить пирамиду можно с помощью)
plottools[polygon]
>?plottools[polygon]

@Carl Love 
of course, you suggested a general approach.

f:=x->((4*x^2-4)^4)^(1/5);
evalf(f(0));

@panke  I type  ?dsolve[events] then press Enter and receive a detailed description.

@panke 
 

restart; 
dsys1 := {x1(0) = 0, x2(0) = 1, diff(x1(t), t) = 1, diff(x2(t), t) = t}; 
dsys11 := dsolve(dsys1, numeric); 
plots[odeplot](dsys11, [t, x1(t)], t = 0 .. 12);
 plots[odeplot](dsys11, [t, x2(t)], t = 0 .. 12); 
dsys := dsolve(dsys1, numeric, events = [[x2(t) = 5, [halt]]]);
plots[odeplot](dsys, [t, x1(t)], t = 0 .. 12); 
plots[odeplot](dsys, [t, x2(t)], t = 0 .. 12);

@nm  Information just in case, perhaps, will be useful. Look at the differences.

Example:
nops(solve([x^2+x*y-1, y+1], [x, y]));
and
nops([allvalues(solve([x^2+x*y-1, y+1], [x, y]))]);

@Adam Ledger You also missed [ ]  in my answer

@nm  You missed [] in my answer.
Maple 17

@Fabio92  Of course, there are fundamental differences in the construction between precision machines and manipulators. But there are materials, for example, wood, plastic, styro foam and the like, where, it seems to me, the use of a manipulator is quite possible as a CNC. That is, yes, the idea is more mathematical than technical.
Thank you for your clarification. My English exists by help a Google  translator only.

I especially thank you for your full understanding of the idea, and it's nice, because I very rarely manage to explain anything even in Russian.
 

@Fabio92  Are you sure you understand the proposed method? The angles are always uniquely determined. Because this is how the model is made-manipulator-trajectory. But this does not mean that there is always only one solution for the same point. It's just that we are able to model this way. Believe me, I would not begin to make messages about inverse problem.

I think that the whole complex of tasks related to the solution of the manipulator's inverse problem can be performed directly in Maple. It will be faster and even more convenient than in specialized CAD. Some known schemes of manipulators are ready for testing; it remains only to perform the formalities associated with the recording of control programs.

Because:
1,  It is clear how to make a mathematical model of a manipulator. And for this there are several examples.
2.  The problem of finding the starting points of motion is conveniently to perform using Maple graphics  and with solve or fsolve functions, for example, in a separate program.
3.  The solution of the direct problem is simply routine programming.

Of course, I may be wrong, but for some reason it so seems to me.