A better test of the solution is to plug in the solution on the left, subtract the constant, then simplify. Getting 0 verifies the solution. Maple's simplify is more likely to be able to simplify something to 0 than to some other constant.

@stefano91 I know what "the min and max values of a function" means; there's no need to go into detail. You still need to install the external package DirectSearch because there's no reliable built-in Maple function for computing the global extrema of functions as complicated as yours.

Since you want abs(min(f(x))) and abs(max(f(x))), change the final command to

abs(DirectSearch:-GlobalOptima(Fm(x), [x = a..b], maximize)[1]);

Please note that abs(min(f(x))) is a very different thing than min(abs(f(x))) and that your Question was ambiguous about which you wanted. Indeed, it's possible that abs(min(f(x))) > abs(max(f(x))).

And you want the local extrema also? How many local extrema? And do you want the x-coordinates at which all these extrema are attained? To return these multiple values, I need to know how Excel's =maple(...) command deals with multiple values. Does it expect a list? a Vector? an expression sequence?

@Kitonum The OP's intended expression is sqrt(1-r^2*exp(2*I*theta)). He wrote the expression in LaTeX. The backslashes are not meant as division but rather are the LaTeX escape character.

What do you mean by "simplify"? As far as I can tell, the expression is already in its simplest possible form. So show me the result that you can get by hand, and I'll see if I can get Maple to do it.

@John Fredsted Using a variable is still (somewhat) based on the (temporal) order of execution, not the (spatial) arrangement of commands in the worksheet. It'll only work if you have no intermediate restarts and give unique (and preferably sequential) variable names to the output of every command that you want to refer back to.

See ?Wrightomega.

@Markiyan Hirnyk Yes, but my Answer is based on the exact plot3d command used by plots:-complexplot3d. This can be verified by

subs(plot3d= P, eval(`plots/complexplot3d`))(f(z), z= -2-2*I..2+2*I);

P(abs(f(x+I*y)), x = -2 .. 2, y = -2 .. 2, color = (1/2)*(argument(f(x+I*y))+3.14159265358979312)/Pi, labels = [Re(z), Im(z), ""])

If you make your relevant Reply into an Answer, I'll vote it up.

@mmcdara I just tried in Maple 16, the only other Maple that I have access to right now, and my code works. Try putting restart in its own execution group. A restart should always be in its own execution group; sometimes (and unpredictably) the restart is not fully performed when there are other commands in its execution group.

The following makes no difference to me, as the code already works for me, but try putting the second LinearAlgebra in forward single quotes: 'LinearAlgebra'.

Please let me know how that goes. I want to get to the bottom of this.

@Alsu You can upload a file (worksheet and some other file types) or a plot or animation by using the green up arrow that is the last item on the second row of the toolbar in MaplePrimes editor. You can make a hyperlink by selecting some text and then clicking on the chain icon, the second item in the second row of the toolbar.

Your animation on the left of the book flipping open shows quite a bit of mathematical sophistication. I'd like to see the Maple code for that.

@MrYouMath It can't be done without executing the previous line. "Previous" means temporally previous, not spatially previous.

@sand15 You wrote:

The reason why LEGEND and COLOR do not behave in the same way is a mistery for me  (have you such explanation on your side ?)

It makes sense for a whole plot of many curves to all be one color; it does not make sense for a whole plot of many curves to have one legend entry.

@Carl Love I see something in the HTML that leads me to believe that the webpage tries to resist being contacted programmatically.

@mmcdara I checked again, and it works for me in Maple 2016. What version of Maple are you using?

Hmm, the HTTP status code 301 means that the URL has been permanently redirected. The following string should, I think, be the new URL. You got the empty string...doesn't make sense.

However, when I try your Get command, I get a normal response: code 200, followed by a string of 52852 characters of HTML, followed by a small table. Perhaps you should try again.

Update: On three subsequent attempts, I got the same result as you did. Oh, well.

That's thin content for a Post. Did you intend to say more or to upload a file or to make a hyperlink?

Nonetheless, I encourage your project.

Update: It should be noted that the example animations hadn't been added at the time that I posted the above comment.