I separated the construction of the data from the processing, to illustrate some performance differences in approaches to the latter.

I repeated both (and iterated each a few times).

Download thread_map_acc.mw

The Description in the Help page for topic alias states clearly:

Because aliases are resolved at the time of parsing the original input, they substitute literally, without regard to values of variables and expressions.  For example, alias(a[1]=exp(1)) followed by evalf(a[1]) will replace a[1] with exp(1) to give the result 2.718281828, but evalf(a[i]) will not substitute a[i] for its alias even when i=1.  This is because a[i] does not literally match a[1].

You are trying to use alias for a way that directly goes against that.

It would work to parse strings made afresh, but that would be crazy. For example,

Download allvalues_ac.mw

Names in Maple can be more than one letter long.

When you write xy without any space or multiplication symbol you are writing a name (of length two, using two letters). That is not the same as x*y .

So, for example, 9*xy^2*x^2 is not the same as 9*x*y^2*x^2 .

If you intend x*y and y*z then enter them that way, and do not enter xy and yz which are simply two other names unrelated to x, y, or z.

You can use Edit -> Find/Replace from the menubar to change them easily.

The documentation states that colorscheme with xyzcoloring is available for 3D surface shading, and thus not spacecurve, does it not?

It is possible to accomplish shading of spacecurves with custom functions of the parameter or x,y,z coordinates. One way is to do construct the whole thing, somewhat like I did here. There are other ways.

You are missing a multiplication symbol between the round brackets.

Without them your input is parsed as function application, rather than multiplication.

Another choice, in 2D Input, is to use a space to denote implicit multiplication. But that approach is error-prone, since it is difficult to distinguish visually.

Download 2d_mult.mw

If you want "gridlines" which illustrate the idea of rotation then why not use a non-cartesian (and suitable) coordinate system?

For example,

Download cylindrical.mw

I used a solid Pink above for the color of the gridlines, but you could change that to color=u so that they were colored by angle (or whatever other radial function you prefer). That covers one of your queries, it seems. For example,

Download cylindrical2.mw

I don't know why the transparency option isn't effective with fine granularity, eg. for small values.

It would be more useful if the "gridlines" could be rendered on a coarse grid but computed using the finer grid -- so that the surface and lines match.

If the grid dimensions are odd then the wireframe produced in other Answers (using cartesian coordinates especially, for this particular example) will not match the (finer grid) surface properly.

[edit] For your approach of drawing the curves manually (in lieu of wireframe grid lines), you could generate them in another coordinate representation (eg, theta and z), coloring them by a function of theta say, and then transform to the cartesian coordinate plot. That would also give you your radial or cylindrical lines with either being shaded by angle. I don't think that your expectation makes good sense: to compute and draw the lines in cartesian coordinates while expecting a mechanism for shading radially. If you want them shaded as a function of angle then use a suitable coordinate system.

The problem with literal subscripted names (and showassumed=1 for trailing tildes) occurs with the extended typesetting level.

It apparently does not occur in my Maple 2019.2 for standard typesetting level. So that may be another workaround, see attached: assumed_literalsubscript.mw

The behavior seems to involve complicated interplay between the GUI and the Library Typesetting.

You need to specify which property of the ListBox you're trying to set. The property value denotes the selected item.

Eg,
   SetProperty("ListBox0", itemlist, convert(DataSet[..,1],list));
   SetProperty("ListBox0", value, DataSet[2,1]);
   SetProperty("ListBox0", value, DataSet[1,1]);

Also, load the package using with as a command, without any space before the opening bracket (or else it will be parsed as implicit multiplication in 2D Input mode). Or utilize the long form, eg.
   DocumentTools:-SetProperty("ListBox0", value, DataSet[1,1]);

LB.mw

There are various ways to accomplish this, depending on whether you want to be able to utilize expression form versus operator form.

>  restart; >  points :=  <<0.4000|  10.0000>, <0.7000|   10.0000>,             <1.0000|  10.0000>, <0.3000|   30.0000>,             <0.4000|  30.0000>, <0.5000|   30.0000>>: >  Data := <0617,0767,0220,0444,0692,0789>*0.001: >  intmethod := LinearInterpolation: >  g := Interpolation[intmethod](points(1..-1,1),Data): >  g(sqrt(2)/2); # observe Error, (in ModuleApply) unable to store '(1/2)*2^(1/2)' when datatype=float[8] >  g(evalf(sqrt(2)/2)); # observe >  plot(g(x),x=0..1, size=[400,200]); >  e := x/sqrt(2); >  G := unapply('g'('evalf'(x)),x,numeric): >  G(e); >  g(1), G(1); >  G(sqrt(2)/2); >  F := 5+G(e)*x^2; >  eval(F, x=1); >  plot(F, x=0..0.1, size=[400,200]); >  Optimization[Minimize](F, x=0 .. 1);   Here are some other ways...   >  f1 := unapply(5+'g'('evalf'(e))*x^2,x,numeric): f1(1); f1(x); >  plots:-display(Array([   plot(f1, 0..0.1), plot(f1(x), x=0..0.1) ]), size=[400,200]);         >  Optimization[Minimize](f1(x),x=0 .. 1); Optimization[Minimize](f1, 0 .. 1); >  #plots:-display(Array([ #  plot(f1, 0..1), plot(f1(x), x=0..1) ]), size=[400,200]); >  f2 := proc(xx) if not xx::numeric then return 'procname'(args); end if;                      5+g(evalf(eval(e,x=xx)))*xx^2;             end proc: f2(1); f2(x); >  plots:-display(Array([   plot(f2, 0..0.1), plot(f2(x), x=0..0.1) ]), size=[400,200]);         >  Optimization[Minimize](f2(x),x=0 .. 1); Optimization[Minimize](f2, 0 .. 1); >  #plots:-display(Array([ #  plot(f2, 0..1), plot(f2(x), x=0..1) ]), size=[400,200]); >  ee := unapply('evalf'(x/sqrt(2)),x,numeric): >  f3 := unapply(5+'g'(ee(x))*x^2,x,numeric): f3(1); f3(x); >  Optimization[Minimize](f3(x), x=0 .. 1, method=branchandbound); Optimization[Minimize](f3, 0 .. 1, method=branchandbound); >

Download convert_interpolation_object_ac.mw

Are you trying to change your setup so that input as in 1D plaintext Maple Notation in a Worksheet (which happens to default to red input)? Carl's Answer shows how to accomplish that.

Or are you trying to change the color of typeset 2D Input from default black to red (in your choice of Document or Worksheet)? If that is your situation then use the main menubar and select,
   Format -> Styles...
then in the popup scroll down and select
   2D Input
then in that popup push the button
   Create Character Style
and in the next popup push the Color button.

If you modify some such aspect of the Style then you can also make that Style set as default moving forwards in new sheets, using Format -> Manage Style Sets...

See also the Help page with Topic
   worksheet,documenting,characterstyles

Apparently it relates to whether the floating-point exponent in a call to `^` matches the type of the base.

It seems to work if the float exponents are cast to complex floats. I got the "expected" result in either of these ways:
1) instead of exponents like 1/beta I used Complex(1/beta,0.0) , and similarly for the others
or,
2) I specified the procedure's parameters alpha and beta as complex(float) rather than float.

I consider this a  bug, and will submit a report

note: I think that your code and operations could be simplified, with several steps combined, etc. I haven't done any of that.

Download Compile_proc_ac.mw

You assigned the result to cSos.

You then tried to call cSoS.

Note the capitalization.

I am surprised that the VolumeOfRevolution command doesn't accept options to specifiy the initial and end angles.

Anyway, for fun,

restart;
with(Student:-Calculus1):
with(plots):
kernelopts(opaquemodules=false):
foo:=eval(VolumeOfRevolution:-ModuleApply):
animate(A->subs(2*Pi=A,eval(foo))(cos(x)+1,x=0..4*Pi,output=plot),
        [A],A=0..2*Pi,paraminfo=false);

Here are attached two more ways.

One uses Explore, since the regular animation frames can be heavy on GUI resources.

Another gets an animated effect by calling Tabulate within a loop. I include this because by various tricks it allows a long 3D plot to be displayed (scaled) without all the usual empty white space above and below.

QuestionAnimationVolumeOfRevolution_ac.mw

The following will export the plot to a file p1.png

You can choose other formats (eg, gif, bmp).

You can utilize the cat command to form the filename (including some location in your filesystem). If you utilize a relative path in the filename, or just a simple filename like the example below, then it will use currentdir() as the base location.

The inline setting puts things back to normal, where plots get displayed in the GUI.

restart;
P:=plot(sin(x),x=0..Pi):
plotsetup(png, plotoutput = "p1.png"):
print(P);
plotsetup(inline):
print(P);

See the Help page for topic plotsetup . And alternative is to use the Export command, which also has a help page with a plotting example.

You don't have to use the use the print command for code at the top-level. But that's what you'd want if running this inside a procedure.

And, of course, you don't also have to output the plot in the GUI as in the last line of the example above (since that's problematic for you).

Whether this solves your problem will depend on whether it really was due only to the inline rendering of the plots.

Up until Maple 2015.2 I get,

  piecewise(1 <= n and n < 10,2^(1-n)*product((-1)^n0*(n0^2+n0-90)/(n0+1),n0 = 1 .. n-1),0)

And from Maple 2016.0 up to Maple 2019.2 I get that unfortunate result.

However,

Download rsolve_hmm.mw

It seems weird, to be calling rsolve with such an assumption.