@Rouben Rostamian

This worksheet, like all your previous replies to my Maple Primes questions, gives me valuable new insights which I greatly appreciate.  

@dharr Thank you for your enlightening answer. I will study it more thoroughly for additional insights.

@Rouben Rostamian  What you say makes sense. Then this is the first time I've read a math assertion in Wikipedia and other web sites that is not true.

@Carl Love Thanks for the hint, but that didn't work either.

Could there be a problem with the worksheet name? It is several words connected by underscores. 

@Mac Dude Thanks for pointing out that both Int... expressions describe the same plane.

Can you refer me to other examples of plotting of a procedure so I can learn more of this technique?

Supplementary question: Is there any way plot options can be selected in the plotted procedure and implemented in the plot command?

For example, each of the plotted part spheres could be displayed with its own color. 

@tomleslie Thank you. I was not aware of the int(Integrand... technique.

@dharr Your answer will help me solve a problem I'm working on

@Carl Love Thank you. I'll modify the integrals as you suggest

@Kitonum In my original question I omitted the role of density.

Does your answer (as corrected) assume a uniform density of one? How does your answer change if the truncated ellipsoid has a uniform density other than one?

@Kitonum Your answers are always clear.

@vv Your answers are always helpful.

@vv Thank you and I apologize.

I just realized that I used acceleration derivatives where the correct operations are velocity derivatives.

For interest sake, what do A and B represent in your reply?

@tomleslie 

ShadeVertical.mw

@tomleslie Thanks for your detailed reply.

1) I have removed command Picture which was left in the worksheet in error.

2) Several of the executions of procedure ConstructCircle give incorrect results in your PCTiling.mw. I do not know why.

    Here is a corrected version of Poincare_tiling. It executes with correct results this morning on my machine; I can only hope it does so for you as well.

If not, then perhaps all you can do for me, if possible, is to direct me to a source that I can learn from showing one or more implementions of the transformation formula.

Poincare_tiling.mw

@tomleslie I thank you first for the helpful observation and then for your detailed answer. 

It will take me some time to digest this and I may have follow-on questions.

I am new to hyperbolic geometry and only recently learned how to create a hyperbolic circle and a hyperbolic line through any two points in the Poincare disk. This is a fascinating branch of geometry!