For anyone else answering, the top has a uniform density of one.

@acer Your suggestion works well and is more intuitive to me. I would like to praise your answer but I don't see a thumbs up or trophy icon in its header.

@Carl Love As usual, your answer is informative and to the point.

@Carl Love Hello Carl, I've examined all the ListTool commands but cannot find help text for operator ?[] which you used above. Is help available and if so how can I find it?

@Carl Love Thank you, Carl for the insight into the light ray vector and for several list manipulations in Maple that I was not aware were possible.

Sorry, plot3d parameter Plot3Daxes from my archive displays boxed, colored axes.

@Kitonum I have gratefully learned several coding techniques from your examples. Thank you.

On examining an open umbrella, it appears that the surface between a pair of ribs in not a portion of a sphere but a minimal surface.

Is this true? Does any Maple resource (Maple Primes, Maple Application Centre, Maple package) demonstrate or provide the code for calculating and displaying such a surface?

@Markiyan Hirnyk Thanks for pointing me to the appropriate help page, I don't know how I overlooked it.

@Jarekkk I hope you receive this question to an old answer.

The solve commands in your answer above work in Maple 2016.0 but I can't find an explanation of the 'parametric' or 'parameters' options in Maple 2016.0 help.

Where can I find help text explaining these options?

@dharr Both DirectSearch.mla and DirectSearch.hdb were in the path displayed by command currentdir() when I issued the HelpTools migrate command. The .hdb file size is 2711 MB but the migrate command produced a DirectSearch.help file whose size is 56 MB. This small size led me to say that the .help file had no content.

@tomleslie Thanks, but I don't have Maple 2015 having just upgraded from Maple 15 to Maple2016. Is there any other way?

@Kitonum Greeting. It seems the overflow error occurs only in Maple 15.

When the following statement in procedure Picture above...

P[i]:=seq([subs(var=var1+i*h,e1), subs(var=var1+i*h,e2),0], i=0..N) fi; fi; od;  #`  MODIFIED FOR 3 D `[f(t), g(t), 0] 

...  is replaced by ...

if nops(L[i, 1]) = 2 then P[i] := seq(subs(var = h*i+var1, [e1, e2]), i = 0 .. N) else

e3 := L[i, 1, 3];

P[i] := seq(subs(var = h*i+var1, [e1, e2, e3]), i = 0 .. N) end if:

... then the following list displays a pretty seashell shape

L := [[[0, 0, 0]], [[cos(a), sin(a), (1/3)*cos(8*a)], a = 0 .. 2*Pi]]

@Kitonum Entering command interface(version) produced this response:

Standard Worksheet Interface, Maple 15.01, Windows NT (unknown), June 2 2011 Build ID 636299

Could there be a bug in this version of Maple 15?

My operating system is Windows 10. I intend to upgrade to Maple 2016 as soon as it is available.

@Markiyan Hirnyk I emailed WPI several days ago and have received no reply.

@Markiyan Hirnyk Are you aware of any other source describing the commands in package CalcP7, or of any other package providing the same sort of functionality?