@FDS 

It is good that you have clarified that my guess (of difference in methods) was wrong. I was not satisfied with that guess. Carl's amazing solution, from a different angle, demonstrated that we are not dealing with a nonlinear problem which makes solutions less depended on the method.

Your explanations above will help others. If you have not done it yet, you might want to add the mathcad tag in your original post.

Unfortuneately, I cannot provide a more efficient way - neither in terms of simple and compact syntax nor in computation efficiency. My optimization experience is not more than basic. You might want to clarify what is more important to you.

@Traruh Synred 

The forget function is used to clear remember tables of procedures it does not clear the any return values, i.e results of a precedure call. Maybe your procedure invokes other procedures that update their remember tables each time they are called.

Example: If you call sin(1.2345) Maple will only do the calculation once. Next time you call sin with that same argument Maple will return what it remembers. This process makes Maple efficient but can fill up the memory.

@Traruh Synred 

have you tried the forget command on your routine to clear memory?

@FDS                                                                

@MagnusMJ 

Does the Maple.ini file change when you change options (under tools).

Possible file locations are described here help(worksheet,reference,initialization).

You can equally rename the Maple.ini file to test if Maple creates a new Maple.ini file at the next startup.

If it does, we know at least that the GUI can write to the file system.

The GUI is implemented in Java. Do you have other Java installions on your system?

Try also minimizing the Maple Window and change display settings. Maybe the file dialogues are placed out of screen bounds.

@MagnusMJ 

What happens if you click on a Maplefile like Download jrive_ex4.mw , do some changes and then save? Close all files and open the file via Recent documents.Did you use the default settings and folders during installation?

What does "save as" do? Do you get a file dialogue?

Can you at least save to Maplecloud (to My Files) or export files?

(Maplecloud, if it works, could be a temporary workaround.) 

@FDS 

I read

the number one minus a vector divided by a scalar Q0. How to substract a vector form a scalar?

It is the normal behavior of Maple that nothing happens when you press save in the sense that you do not see very much going on (on the GUI). You should not get a "Popup" (i.e. file dialogue) but the file is saved to its original name and location.

Please clarify that file contents does not change after applying changes to a file and pressing save.

Can you provide this Mathcad equation expression in standard math notation

If Q and H are supposed to be vectors, this expression does not make sense to me

Your parameters do not match.

• Le is not in the original equation
• D[t] and D[b] are not functions in the original equation

You have resolve this before substitution and simplification can be performed

I have added a benchmark you have posted to the information of my computer.

Quite intersting.
 

Download Maple_-_computer-info_with_benchmark_.mw

For me it looks like that the author is ignored. I.e.: the search you performed is the same as without Author.

@sand15 

I was about to say no and suggest image processing programs like ImageJ, but the program you suggest is much better for occasional work, since it includes a scaling option.

Works really well!

@Carl Love 

Now the rendering becomes nice.

With transparency polar surface contour plots are possible for quantitative interpretatioin of 3dplots.

👍

@Carl Love 

Up to 24 spokes (15-degree steps) you are right, above the grid shows less spokes and is not regular spaced (e.g. grid=[7,30]). At larger steps the polar grid looks more like a spider web.

Appart from that, it is less work than I expected and the rendering is acceptable (IMO). 
@Jamie128 : What do you think?

p1 := plot3d([r, theta, (csc(theta)/r)^2], r = 0 .. 2, theta = -Pi .. Pi, coords = cylindrical, style = surface, shading = zhue):
p2 := plot3d([r, theta, 0], r = 0 .. 3, theta = -Pi .. Pi, coords = cylindrical, grid = [7, 25], color = white, thickness = 2, glossiness = 0, shading = none):
(2*Pi*i)/24:
seq([3.5*cos(%), 3.5*sin(%), 0, %], i = 0 .. 23):
p3 := plots:-textplot3d([%]):
plots:-display(p1, p2, p3, view = [-4 .. 4, -4 .. 4, 0 .. 99], axes = framed);