@bobvandijk The back-ticks are not visible in the 2D Output if one uses Maple 2023.0 (which is the version that Carl usually uses).

The back-ticks appear in the 2D Output for this kind of subscripted display (double-undescore) in Maple 2022 when using the default setting,
   interface(typesetting=extended):
It is possible to get the atomic name `A__b,c` to display without the backticks visible in 2D Output in Maple 2022, if one uses the setting,
   interface(typesetting=standard):
however I don't particularly recommend that adjusting that to the non-default setting; you might well find something else which you don't care for if you use it.

If you go with the alternative indexed name A[b,c] which also displays as a subscipted name in 2D Ouput then note that you can also enter that in subscripted form in 2D Input mode.

You could do that with the following keystrokes, and a single-underscore:

     A  Ctl-Shift-underscore  b,c

Download sbscr_M2022.mw

It looks like you've used Maple 2015.2, for your attachment.

But the examples work ok for me using Maple 2019.2.1 (or Maple 2023.0, for that matter).

DocumentTools_and_Background_M2019.2.1.mw

ps. I did adjust one of your examples to be a Table inside a Group. rather than in an Input (a minor change, not directly related to your issue).

pps. I suspect that the issue in older versions <= M2018.2 is a GUI problem with actually embedding the content. The content results like InlinePlot(T[1]) seem structurally ok, and decode ok.

Here's one way (given what you've done so far):

dont_get_it_ac.mw

I am not aware of a programmatic facility to set the global FPS that one sees in the Animation part of the GUI's main menubar, dictating behavior for whatever inlined animation may be currently in focus (via the mouse-pointer).

However, if you put your animation into a PlotComponent then you can programmatically set the delay between frames, using the delay property.

That's close (but not quite equivalent) to the reciprocal of FPS, since (I believe) it's a delay from the moment one frame's rendering is finished and the next frame's rendering begins. That's not quite the same as the time between when successive frames rendering begins -- it's not quite the same in the frame itself takes longer to render.

Here's an example in which I inserted the PlotComponent by using the Components palette in the left-panel.

anim_delay.mw

With that approach you can programmatically adjust the frame-delay, from the worksheet, even while it's being played. You can also set multiple animations playing in different components, and adjust their frame-delays separately. You can also set the frame-delay for a component before assigning an animation as its property and start it playing.

You should also be able to programmatically construct and embed the Component+animation, with a delay specified at creation time. In the following example the specified delay doesn't seem to get picked up the first time I play it, unless I stop/switch focus. A pity. However, after refocus it works as intended. And the previously mentioned programmatic controls also work here.  anim_delay_EPC.mw

I might also mention that, AFAIK, for a usual inlined plot/animation, the FPS is not stored as part of the worksheet.

Amongst other solutions, you could use,
   'f'(x)
   Typesetting:-Typeset(f(x))

Your original used `f`, which is just the name f and offers no guard at all against the unwanted evaluation of f(x). using your operator assignment to f.

You might have intended single right-ticks (aka uneval quotes) like 'f', instead of single left-ticks (aka name quotes) like `f`. It might be useful to review the purposes and functionality of Maple's various quotes.

AnnotationDérivées_ac.mw

There are several other, alternative, solutions, including,
   InertForm:-Display('f(x)')
   "f(x)"

Personally, I am not a huge fan of the solutions 'f'(x) and 'f(x)' since the single right-tick unevaluation quotes are ephemeral and can get too easily stripped off by accidental full evaluation (eg. reference at the top-level, passing as argument to procedure call, etc). I prefer the solutions that transform the expression into a pure type-setting kind of construct, which the other two mentioned approaches do.

The above are all programmatic solutions. If you are using 2D Input mode then a mouse-driven, manual, alternative is to select the expression f(x) where it appears at the appropriate place in your input, right-click, and use the menu choices,
   2-D Math -> Convert To -> Atomic Variable

Download TSRule.mw

Here are some adjustments, which seem to allow the it to work in my Maple 2023.0 (especially important being the solve call.)

Download sssss_ac.mw

Here's one way, keeping fractions together, eg. sqrt(3)/2 instead of 1/2*sqrt(3).

I also changed the t15 textplot as an example of how the irrational fractions in those textplots could be handled more simply.

And I added some dotted grid-style lines to show that the tickmarks are passed through.

Adjust, to taste.

CERCLETEST_ac.mw

Firstly, you appear to mean B*r and N*g, but you mistakenly had the two-letter names Br and Ng.

The following gets the float-point result quickly, using the inert Sum and Product commands,

Download brn_ac0.mw

Here's another way to get that floating-point approximation, with an exact special-function representation in terms of hypergeom. (And evalf acts quickly on that hypergeom representation.)

Download brn_ac.mw

The int command has an option continuous that can deal with this example.

Download Eval_definite_integral_ac.mw

You had several syntax problems, eg,
   - You had = instead of := where you were trying to assign to Profundidade
   - You had multiplication symbols before the opening brackets when trying to call SensibilidadeK,
etc.

There may have been other mistakes that I did not find. Check the results.

Download code1_1_ac.mw

That symbol is available from the Large Operator palette.

If you combine it with the Accents and Layout palettes you can construct that as 2D Math. (Optionally your can right-click convert it to an Atomic Variable.)

Download LrgOperator_ex.mw

Are you also wanting it to be hooked up to some specific command, and if so, which, and for what concrete example?

A variant,

A := {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
      47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101}:

select(x->x mod 3 = 1, A);

      {7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97}

Is this OK?

FicheGraphique_ac.mw

You are mistaken in your claim that this is a bug.

If you are studying integration then you should certainly learn about the (arbitrary)  constant of integration, as it relates to examples like yours of indefinite integration.

You should understand that your indefinite integral has infinitely many solutions -- differing, each, by value (that is constant wrt the variable of integration) -- because the derivative of such a constant term is zero.

This is not something special to Maple; it's a mathematics thing.

Download indef_int_ex.mw

ps. Please don't submit both a Post and Question for the same example.