Firstly, you can compare your technique's results with those of the plots:-conformal command (using suitable parameters, of course).  See attached.

Next, we can cobble together a version of multiple calls to plots:-conformal, so that we attempt a shading by hue which is similar to his scheme. (One could also scale the intensity, the "V" of "HSV", but I have not done that.)

Also -- and I expect this may be key for you -- one can compare his scheme on log(z) versus yours for exp(z), and vice-versa, and his for arcsin(z) against your for sin(z). Do that explain the discrepancy to your satisfaction, as a matter of direction of the operation? (I do not know why he chose to display the inverse mapping...)

Download conformalfun.mw

ps. If I were to attempt such a coloring scheme from scratch I'd try and do it more gracefully and efficiently, rather than clumping all these plots:-conformal calls with shared edges (and duplicated calculations). I did it this way partly because I was trying a crude mimicing of his "1/16" block, with your own technique also in my mind, and partly because I wanted to see the end result sooner and with less coding effort.

It seems as if you are trying to find the discrete minimum, for nn a positive integer in 1..5.

If I have interpreted the goal properly, then I suspect that the following might not surprise anyone (where each xx[ii] attaints its lower bound, for each posint nn).

Hence my use of n-n^2 in the first computation below (where even that min and seq call are avoidable if we realize it is decreasing).

Your original formulation is an abuse of the notation and syntax, IMHO. But below is (just) one way to deal with the programming.

Download discr_opt.mw

You could try something like this,

Download q_acc.mw

There are several interesting ways to plot the logistic map, and it's not completely clear from your wording what kind of plot you are after (though I might guess that you might be looking for a straightforward solution, as a beginner in Maple).

On this forum, see here, here, here, and here.

You can also see the Bifurcation command, in more recent Maple versions.

See also here, for the cobweb plot example near the bottom.

This is a fequently asked question.

f:=x->x^2+x^3:

g:=unapply(diff(f(x),x),x);

   g := x -> 3*x^2+2*x

g:=D(f);
   g := x -> 3*x^2+2*x

Let me know if this is the kind of thing that you wanted to accomplish.

I used the DirectSearch ver.2 package for the nonlinear fitting (since the NonlinearFit command does local optimization and without a tight set of parameter ranges it can converge to a local optimum that is a measurably worse fit). You can install the DirectSearch ver.2 package in the Maple 2020 GUI from the menubar's Maple Cloud login, or obtain it from the Maple Cloud website here, or for much older Maple versions install from the Application Center here.
 

Download donnees_cycles_sin_DS.mw

You are encountering an (old, eg Maple 11) evaluation issue in animate.

(The problem was fixed many years/releases ago.)

There are several possible workarounds, for your example in your version.

In your Maple 11, replace the call,

   animate(pointplot3d, [ [b(t),c(t),d(t)], symbol=box, color=blue],t=15..100,
                 background = odeplot(sol, [x(t),y(t),z(t)],t=15..100,numpoints=7000),
                 frames=20);

with,

   animate(t->pointplot3d([b(t),c(t),d(t)], symbol=box, color=blue),[t],t=15..100,
                 background = odeplot(sol, [x(t),y(t),z(t)],t=15..100,numpoints=7000),
                 frames=20);

I'm not sure what you want to do about "c". Do you want it as some new unit, and if so could you specify completely? I'm not sure I understand what you want with "c=h=1".

Download unitsMeVs.mw

The problem seems to lie in how the GUI is attempting to typeset the echoed assignment, where the result from fsolve is NULL (no real solution found).

In particular the problem seems to be that the problematic paragraph in question has had its "Numeric Formatting" set to "fixed" with 3 decimal places. It seems that when the result of the computation is NULL this goes wrong and it mishandles trying to typeset that in the specified numeric format (which is a GUI bug).

I had difficulty fixing it by, say, changing the d_sample value to 4.5 so the an numeric result was attained, toggling off Numeric Formatting (I think successfully), re-executing OK, then changing the value of d_sample back to 4.6 so that no real root would be found. The problem remained. But I was able to reproduce the problem (see at end) in a way that convinces me that Numeric Formatting of the assignment of NULL is the cause.

One way to fix the example is to place a full colon as terminator of the problematic 2D Input line. Then d_cam_solved gets properly assigned NULL, but the problematic echoing of the assignment is avoided.

Another way to avoid the problem is to wrap the call to fsolve in square brackets, eg, [fsolve(...)] so that in the problematic case the result is the empty list [].

Another way to fix the example is to rewrite the whole line (manually), but without setting its Numeric Formatting. But not cut&paste of the input line, as that can inherit the prior Numeric Formatting. See attached.

Download Ray_transfer_matrix_ac.mw

I can reproduce the problem elsewhere. I create a Document with the 2D Input,
   foo:=1.234567
and then execute, and then set the Numeric Formatting to say "fixed" with 3 decimal places. Then I change the 2D Input to instead be,
   foo:=NULL
and re-execute, and this problem appears. I will submit a bug report.

The problem also occurs if the input is in 1D plaintext Maple Notation, if the 2D Output Numeric formatting is so-adjusted, etc.

plots:-animate(plot3d,[[Re,Im](u^4*BesselJ(alpha+4,u)*BesselJ(alpha,v)),
                       u=-12..12, v=-12..12, grid=[51,51],
                       color=[red,blue]],
               alpha=-1..4, frames=50);

Below I make no extra attempt at gaining efficiency (eg. by memoization).

plots:-animate(plot3d,[abs(u^4*BesselJ(alpha+4,u)*BesselJ(alpha,v)),
                       u=-12..12, v=-12..12, grid=[51,51],
                       color=[argument(u^4*BesselJ(alpha+4,u)*BesselJ(alpha,v)),
                              1,1,colortype=HSV]],
               alpha=-1..4, frames=50);

You can use plot(...,style=point) or you can use Statistics:-ScatterPlot.

You can also add options axes=box and a color, and have plot(...,style=point) produce something similar to the ScatterPlot result here.

Sieving out the non-numeric data has an added benefit that the plot determines the horizontal range of the valid data more nicely. 

Download point_plot_undef.mw

Are you trying to do something like this?

Download test_cat_ac.mw

Here is another way to get that effect, using the cat command,

Download test_cat_ac2.mw

I suppose that you might utilize PDEtools:-dcoeff, except that it doesn't show the zero coefficients.

Here is one simple approach (which you could make stronger, adjust, etc).

Download simple_dcoeff.mw

You can write a procedure to handle the task.

This is for the specific form Int(Sum(...),...). If instead you have a form like Int(A+B*Sum(...),...) then you'd have to enhance the procedure, or first massage into the specified form (using IntegrationTools:-Expand, etc).

Adjust and strengthen or weaken as needed.

[edit] I made an alteration to allow additional arguments of the Int call, see third example.

Download IntofSum.mw

Suppose that L is a list of your lists. Then,

   plots:-display(map(plots:-listplot,L));