I cannot make sense of what you are attempting to do in your two worksheets.

In your statement you write "I define c by a 3 segment piecewise nonlinear function of H".  Perhaps that's what you intend to do, but your worksheets define c as a function of t, not H.  That's where things go wrong.

Here is a suggestion:

restart;
c := H -> piecewise(...expressions in H...);
H := t -> sin(2*Pi*t);  

Edit the above as needed, and then use c(H(t)) as the coefficient in your PDE.  Write again if problems still persist.

By the way, you have H and Ho in your worksheets.  It's not clear why there are two of them.  Need to explain.

I can't tell what it is that is being plotted.  The code that you have supplied does not help.  To get useful help, state the objective in words.

@Andiguys As far as I know, the save(names, filename) command writes to and reads from filename in the current folder, unless you specify filename as a path to some other folder.  At least that's how it works in Linux.

Perhaps in Windows, filename needs to be given with an "m" extension, as in
save(p1, "p1.m");

I don't have Windows, so that may or may not help.  Try it.

Someone else who may have access to Windows may give more useful information.

@acer Oh, I see.  Your previous comment did not quite register with me, but now I see what you mean.  Thanks again for the explanation.

@acer Thanks for pointing out the overrideoption option.  I didn't know about it and I see that it can be useful.

On a related topic, do you know whether it's possible to set linestyle=dash in plottools:-contourplot?  I get solid lines only, no matter what I try, as in:

p1 := contourplot(x^2-y^2, x=-1..1, y=-1..1, linestyle=dash);
display(p1, overrideoption, linestyle=dash);

I don't quite know how to do dashed lines in a contour plot.  Here is how to do with solid lines.

At the end of your file case1.mw, add the two commands:

p1 := plots:-contourplot(func(x,y), x=0.03..0.15, y=0.02..0.1,
    colorbar=false, contours=conts,color="Red");
save(p1, "p1");

This will produce the contour plots and save the result in a file named p1.

Do the same in case2.mw, but replace the two occurrances of p1 with p2, and change "Red" to "Green".

Do the same in case3.mw with p3 and "Blue".

Then start up a fresh Maple worksheet and enter:

read("p1");
read("p2");
read("p3");
plots:-display(p1,p2,p3);
 

@nm Download the file Maple2025.2LinuxX64Upgrade.run from Maplesoft's website, and then in a terminal execute the two commands:

    chmod +x Maple2025.2LinuxX64Upgrade.run
    ./Maple2025.2LinuxX64Upgrade.run

The first command makes the file executable.  The second command executes its instructions.

@Earl Sure, just add a little bump near the center of the top face of the moving block.

@acer That's a nice construction.  The hemisphere may be plotted more efficiently in spherical coordinates.  Then there won't be a need to for an excessively fine grid.

As to your question "is the base circle/edge of his hemisphere ragged" regarding the answer posted by janhardo, the answer is no, it's not jagged in his third version, since the hemisphere is plotted in spherical coordinates.

@janhardo That's a very good, regardless of whether it's done by you or by an AI :-)

@janhardo Yes, but is there a hole on the surface once you set transparency to zero?

I can confirm that the scrollbar's up and down arrows are missing in Maple 2025 (on Linux).  That's a pity

I consider Maple 2025's funky interface altogether a badly misguided experiment.  I am staying with 2024 until the old sensible interface is offered as an alternative in a future release.

@michele In the absence of a worksheet, it's anyone's guess as to what you may have done wrong.  To get a useful feedback, post the worksheet.

Regarding:

    From these, the sphere's radius r and the coordinates of its center can be determined?

Which sphere?  There is no sphere in the question's statement.

Plot the sphere that passes through the point (5,1,4) and intersects the coordinate planes x=0, y=0, z=0 in circles of radii 1, 2, and 3, respectively.