Get a good copy from https://www.maplesoft.com/ but you need to pay for it.

I run Maple on Ubuntu Linux and I am not unhappy with the default look and feel.  Does it really look awful on Arch-Linux?  Post a screenshot to let people know what it is that you see.  It will also help if you describe what it is that bothers you.  Otherwise it is difficult to provide useful advice.

@Earl Since you said that you want to animate the solution, you may be interested in this which I am posting without its Maple code.

The help page on the sign function says

    The sign function works for polynomials with coefficients of type `numeric`.

Applying it to expressions other than polynomials goes against sign's intended purpose.

Despite what the legend says, the graph that you have shown is that of the tan function, not the inverse tan.

Moreover...

Tickmarks in the form of multuples of Pi makes sense on the horizontal axis but not on the vertical.

@vv That's a very nice .  It also explains why understanding that object is not so intuitive.

Consider these two objects:

#1. A thick/solid mobius strip printed on a 3D printer

#2. A construction of your drawing, made of paper

Object #1 is a one-sided surface in the sense that it's impossible to color it in two colors without discontinuities

Object #2 is a two-sided surface!  It can be colored continuously in red on the side of the paper to which the arrows are glued, and in a different color on the reverse side of the paper.

It's the dichotomy between #1 and #2 that makes it difficult making conclusions without a careful drawing such as yours.

@vv The mathematical zero-thickness mobius strip is certainly not orientable, and therefore it cannot have a continuous normal.  But a "thick" mobius strip is different.

If you follow the normal vector as it turns one round around the thick strip, it ends up in a point opposite its starting point but at a distance T away from it where T is the strip's thickness.  The vector's orientation is reversed but its point of application is not the same as that of the starting point, so there is no discontinuity.

If you continue traveling with that vector for another round, it will arrive at the starting point and regain its original orientation.

I have printed a few mobius strips on 3D printers.  They pose no difficulties.

@JoshuaLeiter I cleaned up my Maple code and presented it as a Post.

The code does parametrized surfaces only.  Unfortunately it cannot handle implicitly defined surfaces.

@Kitonum I have used essentially what you have shown in order to produce 3D objects on a 3D printer.  Let's name your plot P. We save it as an STL file in Maple through
Export("filename.stl", P);
Then send the file to the 3D printer.

That method works sometimes, and fails at some other times.  Here is why.

The STL file is expected to contain a triangulation of the object's surface.  Maple's Export()  produces that triangulation.  The STL file is also expected to include an outward unit normal associated with each triangle.  Maple's Export() fails to do that — some of its normals point outward and some point inward. That obviously confuses the printer which then produces junk.

One can import the STL file produced in Maple into the freely avaiable mesh viewing/manipulation program MeshLab.  In MeshLab, surfaces which have properly defined outward unit normals are rendered in white.  Surfaces whose normal are incorrect are rendered in black.  I exported your Maple plot to STL and loaded into MeshLab.  Here is what we see:

We see that half of the surfaces and edges are in black, indicating that their normals are incorrect.

I gave up in using Maple's Export() for 3D printing some time ago and wrote my own triangulation and export routines.  They work quite well and I have printed a lot of 3D objects using them.  My Maple code, however, is undocumented and disorganized. I have been meaning to clean it up and post it at some point. Perhaps this discussion will motivate me to do so.

@nm Regarding the two differential equation
diff(y(x),x)^2 + y(x)^2 = 1
in my previous message, I must point out that of Maple's solutions y=1, y=−1, y=sin(x+c) and y=−sin(x+c), the last two are actually the same sin(x+Pi)=−sin(x).

Furthermore, there are infinitely many other solutions that one may piece together from those. For instance, the colored part of the diagram below represents a solution of the differential equation:

Similarly, in the case of the second differential equation
y(x) = x*diff(y(x),x) + 1/2*diff(y(x),x)^2
whose solutions are y=−x^2/2 and y=cx+c^2/2, we may produce infinitely many other solutions by piecing together the graphs of the regular and singular solutions, as shown here:

This latter example has an interesting implication — it allows solving a two-point boundary value problem such as
y(−2)=a,  y(+2)=b
for reasonable choices of a and b.  This is rather unusual since the equation is of the first order!

@nm Since you are curious about such issues, you may be interested in looking at Maple's solution of
diff(y(x),x)^2 + y(x)^2 = 1
and seeing how you would go about obtaining that by hand.

Once you are done with that, look at this more challenging one:
y(x) = x*diff(y(x),x) + 1/2*diff(y(x),x)^2

 

@Carl Love After dropping the eval:
 

plots:-animate(
   plots:-arrow,
   [p, ptan, width= 0.3, length= 4], s= 0..3,
   background= plots:-spacecurve(p, s= 0..16*Pi, color=red)
);

@Carl Love The purpose of the OP's example of the Determinant outside of the proc is to demonstrate that the definition of Determinant is confined to the proc, i.e.., it does not leak.

@ecterrab Regarding your suggestion for reorganizing the casesplit help page, I am afraid that's too far beyond my realm of knowledge for me to be of help there.  I don't even know what "differential elimination" means, and that appears to be central to what casesplit does.  Nevertheless, a few examples that I have seen of the uses of casesplit indicate that it's a valuable tool and deserves to be brought to the Maple users' attention.

@ecterrab Thanks for your responsiveness to this and all other issues that are brought to your attention.  You are an invaluable asset to Maplesoft.