The word stylesheet is an option of the GraphTheory:-DrawGraph command.

The term Style Set relates to customized character/paragraph attributes, and files to manage them.

In Maple 2026, see the Edit tab in the ribbon, which contains two items:
    Styles
    Manage Style Sets

You can get to the documentation for Style Sets with a query on styleset .

ps. If you query just style in the Help-system then the item for this appears a little too far down for my taste.

The What's New pages show for that latest version that the Online Help has been updated.

But the older What's New pages are also there, with a somewhat standarized naming scheme, reflecting that of Topic names in the Help system of Maple proper. 

So it seems like one could query and see which is the highest such that's present.

Download online_ver.mw

I don't know when they'll be updated next, or the answers for your two queries 1), 2).

If continuity in a solution is important to you (for, say, real x),

Download nm_ode_x.mw

Try the location documented on the Help-page for the user's preferences file.

[edit] Btw, did the site from which you downloaded the installer have a checksum listed for the installer file? Slim chance, but might be worth a check.

The default for Normalizer is that it just calls normal. That is not strong enough in the case of your example that contains exact radicals.

If the exact radicals are removed by applying evalf, then your example runs ok.

If Normalizer is set to something strong enough then your example runs ok. Eg,
    Normalizer := simplify:

inscribe_circle_ac.mw

Note that Testzero calls Normalizer. This pair are key in some linear-algebra kind of operations (eg. finding valid pivots, etc.) Failing to correctly notice a "hidden" zero, due to a weak test, is a classic problem. I haven't yet looked for the particular code line(s) where your example goes awry under simplex, but this kind of issue is not unheard of.

Optimization uses just floats, so it doesn't see this particular issue in the case of radicals. Some things like LinearAlgebra:-LUDecomposition make an attempt at temporarily strengthening Normalizer depending on the nature of the exact expressions found. But not all older commands do.

It seems that the expanded ln term on the rhs is the problem.

By utlizing combine on that term, either solve or RealDomain:-solve can be used.

These work quickly,

Download nm_solve_01.mw

Here are various ways you can evaluate the fitted polynomial at arbitrary values of the independent variable.

You can do it with or without forming the polynomial explicitly. You can do it using procedures or eval. And, if forming the procedure explicitly, you can do it with expanded form or Horner form.

The very simplest way (shown at end), is to simply pass an extra name as an argument to the command, and have the command return the explicit polynomial rather than (as you had it) a Vector of the coefficients:
    Statistics:-PolynomialFit(10, X, Y, x)
See also the Help-page, which also describes a returned solution-module which can access various statistics, etc.

And you can then evaluate it for single values, or map that across the elements of X (or any other Vector).

Here are several of those choices. The second to sixth ways include forming the polynomial explicitly. It's your choice whether to also convert such to Horner form.

I also show the ~ syntax for so-called elementwise application of commands, which is a terse way to apply the evaluation across a Vector such as your X.

Download regr_fun.mw

You had misplaced extra double-quotes in your color strings, eg, ""Red".

The markup for those subscripted items is a kind of name, and with the special characters such names have to be enclosed in single left-ticks (aka name-quotes in Maple). Eg,

    `#msubsup(mi("π"),mi("r"),mn("B"));`

and not just (as you had it),

    #msubsup(mi("π"),mi("r"),mn("B"));

which gets interpreted as a comment since the # is bare.

nb. Those left-ticks might not(!) show in the rendering on the inlined worksheet below. See the attached worksheet in actual Maple.

Download Graph_legend_error_ac1.mw

You could look at this general support page, in the section (near the bottom) titled "Contact Technical Support". There are three phone numbers there, for different geographic regions.

Note the effect of wrapping the Re and Im calls by evalc.

Download wingho_1_ac.mw

Download TESTE_ac.mw

You can use the caption option for that, and one way to construct that from your DATA values would be using sprintf.

caption=sprintf("sigma=%.1f, Cn=%.2f, Crm=%.2f, b=%.2f",
                eval([sigma,Cn,Crm,b],DATA)[])

Q_legend_ac.mw

Or, if you'd like that any/all of those names pretty-printed, eg. sigma rendered as the Greek letter glyph,

Q_legend_ac2.mw

note: I have deliberately not merely used uneval quotes (single right-ticks),
because those are ephemeral, and if you later assigned to any of those
names then an evaluation of the plot construct would result in the caption
turning into, say, 0.65=0.65, etc. Maybe unlikely, but that's defensive programming. Q_legend_ac3.mw

[edit] Yet another reasonable way to construct the caption, and to guard names against further evaluation, involves using InertForm:-Display. This too pretty-prints the sigma character as the Greek letter, etc. This might even be my preferred way, over the 1st and 2nd ways. Q_legend_ac4.mw

This duplicates each frame three times (to slow down the exported .gif file).

It reduces the line thickness as n increases.

Download graph_anim01.mw

Or, with labelled vertices, up to n=50, with just two repetitions per frame, and with lines getting thinner slightly more slowly.

Download graph_anim02.mw
 

Here's an example for the legend, and making the axes' labels and tickmark values bold.
 

Q1_3_ac.mw

I look forward to reading about what other bits you might have forgotten to mention.

The title option seems to have been broken in Maple 2023. It works ok in Maple 2022.2 and earlier.

I will submit a bug report.

The problem seems to be simply that a new outer Table (hidden borders on those inside it) was put around the assembly. And the title is still being put on the a Table that is just inside that. But the GUI only shows Table caption & title on the outermost of a collected of nested Tables. So the title's being attached to the wrong Table now, and not shown in consequence.

Here are two workarounds:

1) Use Explore's overview option instead (adjusting the padding, for the width),

Explore(plot(a*sin(b*t),t=0..10),
   parameters=[[a=1..20], [b=1..20] ],
  initialvalues=[a=6,b=5],placement='right',width=300,
  'overview'=cat("\n"," "$32,"My Explore"));

2) Utilize a (re-usable) procedure instead, which constructs the xml, fixes it up, and embeds it,

NExplore := proc(U::uneval,{title::string:=""}) local temp;
 temp:=XMLTools:-FromString(Explore(U,_rest,insert=false,returnxml=true));
 DocumentTools:-InsertContent(subsop(1=_XML_Table("captionalignment"="1",
   "title"=title,"captionposition"="0","drawtitle"="true",
   remove(type,[op([1,..],temp)],
          identical("captionalignment","title",
                    "captionposition","drawtitle")=anything)[]),temp));
 return NULL; end proc:

NExplore(plot(a*sin(b*t),t=0..10),
         parameters=[[a=1..20], [b=1..20]],
         initialvalues=[a=6,b=5], placement='right',
         width=300, title="My Explore");

explore_title_ex07.mw