Try
 

with(Statistics):
L1 := [2, 4, 6]:
ColumnGraph(L1, axis[1] = [tickmarks = [[0.4 = "abe", 1.4 = "banan", 2.4 = "palme"], rotation = Pi/2]]);

Your general solution Sol1 should also simplify to an expression with signum(xc1-xc2) without the need to restrict the domain to real

sqrt((xc1 - xc2)^2)/(xc1 - xc2);
simplify(%);
                                    (1/2)
                      /           2\     
                      \(xc1 - xc2) /     
                      -------------------
                           xc1 - xc2     

                       signum(xc1 - xc2)
                      

Perhaps the radical is too complex and Maple overlooks this simplifcation or there is no simplification possible in the complex domain (for a reason I can't see at the moment).

Anyway, your substitution is equivalent to the assumption xc1 > xc2. You could use
 

simplify~(solve({eq1, eq2}, [x, y], explicit), radical) assuming (xc2 < xc1)

to avoid a call to realdomain and the substitution step. It's just a little bit neater.

Edit:

No simplification to an expression with signum possible in the complex domain without assumptions because the expression bellow is in general not zero

To change a style, navigate to style under format and modify 2d input this way

See https://www.maplesoft.com/support/help/maple/view.aspx?path=worksheet%2Fdocumenting%2Fstyles

to make it permanet for all worksheets

Without the model it is difficult to help.

In general:

What you have to do is to constrain the end effector position using parameters. There are several ways to do this.

https://fr.maplesoft.com/products/maplesim/modelgallery/detail.aspx?id=38

for example constrains the position a radar points to.

There are videos describing the whole process. Here is one

https://www.youtube.com/watch?v=7IKFqRkKqI0

Once constrained, MapelSim can generate and export algebraic constraints that you need to calulate the inverse kinematics.

The tricky part is to preserve the pulley coordinates in the algebraic constraints. For that you might find the following helpfull

https://www.mapleprimes.com/posts/217390-Equation-Extraction-For-Kinematics

Attached you will find a way in Maple. Since the problem is nonlinear there can be more minima (local or global). That's most likely the reason why the result from Maple and Mathcad do not agree in a first attempt.

NLPsolve (and the Optimization package in general) has a bunch of options Minerr in a solve block does not seem to have. If you want to reproduce whatever Minerr does you have to go through all the options and their combinations. I would start with methods first.

Download SolveBlockQuestion-reply.mw

For comparision:
The best I could do with substitutions. What makes it tricky is the coefficient R1*R2 of s.

I spare out the sorting detail since its already twice as long as acers solution.

Download subsway.mw

Your parameters still do not match. In the following I have tried to show how the substitution should be done and what needs to be changed.

Download parameter_mismatch.mw

In your simple example 

L1 := -L*(k - 1);
collect(L1, L);
                           (-k + 1) L

preserves a "simplified" factor (sign of your original factor has changed). Collect should also work in more complex cases unless there are other sub-expressions where you don't want to collect L. In those cases changing the sign of the factor like this

Lm := (simplify(k*sqrt(L*L)) assuming (0 < L));
L1 := (factor(-L + Lm) assuming (0 < L and 0 < Lm and 0 <= k));

might work as well.

Infolevel confirms that dsolve integrates a first order ode

intde := int(x^2*diff(y(x), x)/(x^2 - 1), x) = int(y(x)^(1/2), x)^(-2/3);
infolevel[dsolve] := 5;
dsolve(intde);
Methods for first order ODEs:
--- Trying classification methods ---
trying homogeneous types:
differential order: 1; looking for linear symmetries
trying exact
<- exact successful

If you additionally increase printlevel up to 50 you will find the ODE (which can also be derived by differention of the original equation w.r.t. to x).

Edit: In this way Maple reduces the inital equation to a first oder equation.

Then appropriate methods are applied

This is the first order integroDE Maple integrates. An ODE without integral that integrates to the same result would be this one

To get there, you have to find a way to convert the right handside of your problem like this (i.e. getting the integration out of the denominator): 

The attachment shows where the above right hand side comes from.

integrode_backward.mw

A base like that with a z-axis?

Any preferences on the ranges?

You did not give a motivation why you use min in your example on a list without units. I  assume that you want to use min on lists with and without units after loading the simple package.

Until the bug is fixed you could call the default environment for lists without units by adding the prefix :- to min:

with(Units[Simple]);
:-min(0, 0);

I run your code in Maple 2023 and have corrected a few errors. What I did is highlighted in oragne.

I had no time to check why A is larger than 1 but maybe my touchups help in further analysis.

A_less_than_one_reply.mw

Alt s with the search term "conic" provides some usefully resources.

For algebraic expressions help(geometry,conic) provides ouput like this:

You may perhaps not have noticed that the call print[-2]() sets the interface variable prettyprint.

Calling print without argument is maybe not an intended use.

I will send a software change request for the interface prettyprint call.
 

Download reset_interface.mw

I tried 2022 and 2023 with the same outcome that you described.

Maybe I found an explanation why Maple.ini does not work:

Any Maple command in Maple.ini, Startup Code and userprofiles is passed directly to the kernel (but not via the GUI).

Typesetting:−Settings(parserwarnings=false): seems to instruct the GUI not to issue a warning on the input (before the command is send to the kernel).

If this is correct, you are looking for a new feature that initializes the GUI. Kind of a GUI.ini or a button (maybe I overlooked it) in the options.