That kind of labeling is available in the Command Line Interface (aka CLI or TTY), and in the Classic GUI.

It is not enabled with default settings in the Java GUI. But it can be enabled by adjusting various interface settings.

Unfortunately the line-breaking doesn't work properly in the Java GUI, for such labeling. Which is a shame because (when working properly) it is a very nice feature. It can make a long expression legible and comprehensible, that would otherwise take many pages to pretty-print.

Download expr_labeling.mw

In some situations the LargeExpression package has some related utility.

And there are also the GUI Equation Labels, which have a different utility.

It's not clear what range for x you wish to allow, or what upper bound for k you wish to consider, or whether you want the plot to illustrate k values.

Here are some ideas. You can solve synbolically for x that make k positive (or not).

Download pw.mw

There appears to be a corrupted Plot XML element (I think in section Opg 3 of Rumintegraler Uge 6).

With that bad element removed, the remaining contents are available, see attachment. This recovers twelve Sections, up to Uge 12. (The Maple 2021.0 GUI could, sadly, only recover the first five of those.)

matOpgaver_1_ac.zip

I strongly suggest that you keep your own regular backups of lengthy and precious assignments done as Maple worksheets.

[edit] I will add this to my collection of earlier reports of corrupted worksheets of Danish students. I'll have to repeat my earlier notes that the manner in which the GUI "repairs" corrupted XML elements could be significantly improved..

@tarik_mohamadi The expression Bi-1 divides both the real and the imaginary components of the determinant expression (eq), under the assumption that remaining parameters are real.

I could get the following (avoiding source=csv, as an option),

Download nm_ImportMatrix.mw

I suggest:

 -- The Programming Guide

 -- Understanding Maple, by Ian Thompson

The first comes bundled with Maple, in its Help system.  The second is relatively up-to-date (2016), well written, brief yet to the point, mostly of good sensible quality, and inexpensive.

If you are going to program in Maple then I suggest you start off by toggling your GUI default modes to:
  -- Worksheet, instead of Document
  -- 1-D plaintext input "Maple Notation", instead of typeset "2-D Math"
(See Tools->Options->Display and Tools:-Options->Interface, respectively.)

How about StringTools:-SubstituteAll, replacing with the empty string?

s:=" \\left \\int x \\,dx \\left":

StringTools:-SubstituteAll(s,"\\left","");

          "  \int x \,dx "

I don't know whether you care about residual white-space,

with(StringTools):
SubstituteAll(SubstituteAll(SubstituteAll(s," \\left ",""),
                            "\\left ",""),
              " \\left","");

          "\int x \,dx"

After issuing stopat(proc1), you need to actually run an example that calls that proc1 procedure. Then the debugger will appear, when the computation invokes that procedure.

I don't think that you should compute the plot as you describe with a fixed z-step-size, eg. by passing the adaptive=false and say numpoints=floor((9-2)/0.5)+1 options to the plot command (modifying how Tom called it). The result would be very coarse.

Tom's suggestion utilizes the default adaptive plotting of the plot command, sampling Z over the range -5..5 according to where it ascertains that more points would help. (This is true whether the z-range is 2..9 or -5..5.)

The computing time for Tom's adaptive plot call can be roughly halved by memoization (eg. storing the fsolve results rather than calling it twice, once for each of x and y).

But if you're willing to experiment with (or compute) the x- and y-ranges then for the example Tom invented even smoother curves can be obtained, and much quicker, eg. through the implicitplot command.

There are also regions in which the plots from the two methods visibly differ (eg. where the curves become steep/multivalued). I leave it to you to judge.

Download impl_fun.mw

Is there a special reason why you haven't provided us with your full example, so that we could test out ideas?

Editing your original.

In the Maple GUI the results from the loop are actually shown for all three of i=1..3 . It's a quirk of this forum that they don't each render when inlined here.

You don't have to use a loop, of course. But I prefer indexed L[i] to concatenated L||i .

Download Lagrange_interpolation_ac.mw

Perhaps more graceful would be a revision to procedure Lg, such that it accepted lxi as an argument, and deduced n=numelems(lxi).
 

(This seems a tiny bit tidier than your followup A_little_example_ac.mw )

You can get more arrows while still using the VectorField command from the Student:-VectorCalculus package (as you've done in your attachment).

You can do that by supplying the fieldoptions option to the VectorField command, using the grid suboption in the list in the right-hand-side.

Adjusting your example,

Download How_to_add_more_arrows_acc.mw

You can read about this in the Help page for the VectorField command. When you encounter a difficulty with some command then a good place to look is its Help page (also available within the Maple GUI itself).

The unwith command is not robust if called within a procedure. (Similarly for the with command.)

Try calling it instead like,

    :-changecoords(....)

which is a reference to the global name due to the colon-minus prefix. That is in contrast to the unadorned name which may have been rebound to some package's export's name, by some prior call to with.

It appears to be a problem with the 2D parser.

If I place the mouse cursor at on the a[0] in that 10th row's existing input, and then delete the space between it and the coefficient 2, then the expected menu appears in the context panel and the context-menu actions work.  Here is the attachment that I got from that.
   Table_solve_issue_ac.mw
The same happens if instead I delete the space following any of the other instances of 2 in that 10th row input.

I could also insert a new, empty 10th Table row, between the old 10th and 9th rows, and successfully retype the whole expression in 2D Input mode, and have it work. I ran into issues with copy&paste.

I don't know whether this problem with 2D Input is actually dependent upon it being a 10th (or later) row.

A GUI Worksheet/Document Table is not the same as the table or rtable Maple (kernel/engine) data structures. So kernelopts(rtablesize) should be irrelevent here.

If you have only the data values (but no longer have the original function) then you can interpolate.

In the following code the colors for the pointplot are (only) interpolated from the hue values of the precomputed (image) data. The function f is not referenced directly for computing the colors in the pointplot; f was used only in pregenerating the image.

datainterp.mw

Note that the extracted submatrix data[..,1..2], and F(data[..,1..2]) both have datatype=float[8], for efficiency in constructing the COLOR plotting substructure.

If the source image resolution is known to be fine enough you might alternatively try linear (rather than spline) interpolation.

Naturally, if you extract H from an HSV image (in the ImageTools sense) then you could accomodate the scaling factor of 360, to get H in the 0..1 range for plotting.

[edit. I've since corrected some use of the dimensions, and re-attached...]

The very long time that it takes for your high resolution example to display is mostly the time it takes for the GUI to render the animation. The kernel (Maple engine) time to compute the plotting structures does not grow nearly as quickly, with respect to the grid resolution.

For example, if I change that resolution to grid=[91,91] then on my decently fast machine the construction of the animation's plotting structure takes 3 seconds but the GUI takes over 100 seconds to render it.

In answering a Question of yours from 5 days ago I explained that the GUI performance is impacted by high resolution of 2D density plots. And that thread had several citations to older posts that mentioned the same issue.

You will not be able to get the GUI to quickly render (using its traditional animation mechanism) a decent number of high resolution densityplots in current Maple, even if they are completely precomputed.

One can get somewhat better GUI performance in rendering a sequence of colored 3D surface plots, displayed with a top-down orientation (view from above) so as to mimic a 2D densityplot. But the performance isn't much better, and the feasible grid resolution not much greater.

Improving the GUI performance for this same example is precisely what this older thread's Answer is all about.

That older Answer uses the background option of the plot command as an alternate for densityplot, but unfortunately the GUI cannot utilize multiple background encodings in rendering a "traditional" plotting animation.

Here are some ways in which the Explore command can be used, instead, to play a sequence of either plots-with-backgrounds or images.

arg_not_densityplot_anim.mw