The isochrone property of the semi-cubical parabola is cited in numerous websites.  It appears that it originated in the Mac Tutor website, and other websites just copied that information without verifying it.  Here is what Mac Tutor says:

In 1687 Leibniz asked for the curve along which a particle may descend under gravity so that it moves equal vertical distances in equal times. Huygens showed that the semi-cubical parabola x^3 = ay^2 satisfied this property.. 

On the face if it, that statement is nonsensical—it says that the vertical component of a particle's velocity sliding down that curve is a constant.  But that can't be true.   Consider a particle released from rest from a point P on the curve.  The intial velocity is zero, and therefore the vertical component of the initial velocity is zero. Later on the particle picks up speed, so the vertical component of the velocity is nonzero.  We see that the vertical component of the velocity changes, so it cannot be a constant, contrary to the Mac Tutor's assertion.

I don't know the correct statement of Leibniz's question and Huygens' solution, but certainly Mac Tutor's formulation and dozens of duplications around the net are not it.

Interesting puzzle.  Here is a clearer restatement.  I have not attempted to solve it.

Download mw.mw

PS: I see that Christian Wolinski has already said the same thing.  Sorry for the repetition.

@acer I thought about doing it that way at first, but did not want to risk it, fearing that eval() may do the two substitutions in sequence, which generally will yield the wrong result.  The help page on eval() says that the substitutions are made simultaneously, so that's reassuring. But in the next paragraph is says that "if there are symbolic dependencies between the expression and the point at which it should be evaluated that are considered unsafe, eval will return unevaluated".  I don't know the circumstances under which this may happen, that's why I chose to roll my own.

@Christian Wolinski Yes, you are right, and thanks for the correction.

If you missed a class where your instructor showed how to write a Maple proc, then see if you can get class notes from a classmate, or better yet, talk with the instructor.

Asking someone to solve your homework problem is not quite the right way to go.  It's you who's supposed to solve that problem, not someone else.

1. What do you mean by "defining the image in relation to a chosen base"?

2. How are the base and T related to the image?

3. You ask "what I'm doing wrong", but you haven't said what you are doing.

I am using Maple 2021.2 on Ubuntu 20.04 (actually Ubuntu MATE 20.04).  I believe that my Ubuntu is entirely up to date. I have no crashing problems.

I suspect that the problem lies in a part of the worksheet that you have not shown.  To help diagnose the problem, upload the entire worksheet, and by that I don't mean cut-and-paste; upload your worksheet as an attachment. Ask here if you don't know how to do that.

@acer Thanks for the details of the redraw option. I don't have 2022, and 2021 does not seem to have it.  I will wait until I get my hands on 2022.

@acer The redraw=false option is new to me.  Where is it documented?  Searched but couldn't find.

Show the progress that you have made toward answering these homework questions, and ask specifically where you need help.

@Carl Love I see.  Thanks for pointing this out.

@Carl Love My reply to the OP was in reaction to his statement that he is finding three local minima and wishes to pick the best among them.  That doesn't inspire me with confidence that he understands the basics of the problem, hence my suggestion.

Forget about Maple for now. Try finding the minima by hand.  You will find that illuminating.

I can't understand at all what you are asking, and apparently neither does anyone else.

It will help if you could give one or two examples, consisting of:what you wish to type into Maple, and the result that you wish Maple to produce.

For example, you may say:

I want to type sin(2*x) into Maple and I want Maple to produce 2*sin(x)*cos(x).