@Christian Wolinski You originally started a Question thread (in which you described problems with lighting options in the Standard GUI, and compared with the Classic GUI in R5.4).

That thread had about 11 responses, links to Rouben's older Question, and other details and examples. It was mostly examples, report, and a very interesting discussion, although you didn't really ask any direct question in it. It appeared to describe a loss of functionality between Classic and Standard Java GUI related to multiple light sources in 3D plots.

You've now said that you deleted that thread (and all that lengthy conversation). Why did you delete it?

Before you deleted the long, original thread (which contained all that information) you also made a duplicate Post, which contained an example from the original threads. Why post the duplicate?

Why would anyone bother taking the time to answer your questions, when you respond to Answers by deleting your original question after the fact?

Was it your intention to call,

     LinearAlgebra:-Determinant(...)

or to load that package before you call its Determinant export?

    with(LinearAlgebra):

    Determinant(....);

and so on.

The problem seems to be this, specifically:

When opening a previously saved Worksheet or Document, the initialization file will not be read following any restart (either from the restart command or via the menubar icon).

Removing any restart call from the beginning of the worksheet does still allow the initialization file to be read, if the worksheet is re-saved and re-opened.

But then the (very useful, and fundamentally common) act of issuing any restart will not cause the initialization file to be re-read.

So, at present in Maple 2019.2, the functionality of restart and initialization files are mutually exclusive for previously saved worksheets.

@Christopher2222 Only one of them can be recognized as the default application for opening the .mw filename extension.

And they utilize the same saved-preferences file. (...and initialization file, depending on set up.) And they recognize any major-version specific toolbox add-ons the same.

But otherwise, they're distinct. Neither uses files from the other's installation directory.

@Christopher2222 What's all this talk about special efforts to unroll an update?

I install every version and point-release separately. It's easy on at least MS-Windows and Linux, at least. Disk space is cheap.

It's not even difficult. When I wanted to install Maple 2019.2 I first installed a separate instance of 2019.0 to a new directory (named "Maple 2019.2"), and then ran the point-release installer on that. And I name the launcher icons appropriately.

On Linux it can also be done by copying (cp -a) whole whole installation directory and then editing the scripts in the bin/ directory to specify the new location.

I ask a sysadmin to do the same thing with the network versions (the easier way, multiple installs).

Sometimes I remove all but the last point-release of previous versions, when a new major release comes out.

@Carl Love I agree. The call trigsubs(cos(6*t),annotate) computes several results, and of course it would be much better to have the request and computation be targeted/restricted.

What work, if any, have you done so far on this homework question?

Have you read the Help page for the plots:-animate command?

@Carl Love The use of f with two meanings in the question is confusing and poor. But it's not what prevented the OP's original approach from working. And it's not necessary to use the different name h in order to get it to work.

The OP's approach failed because he was making operators out of the equations z=blahblah returned by solve, and not accomodating that fact. One way his approach could work would be if he instead used only each RHS formula blahblah from the results returned by solve.

And that's how my Answer works; and it'd still work using f instead of f1 and f2. (Of course it'd be uglier and confusing if it were to so abuse the name f as the original question did.)

Tom's Answer uses a calling sequence of solve without sets, and so the results from solve are scalar expressions and not equations. Thus he avoids the problem with the OP's attempt. Tom's answer would work even if the operator he assigned to h were assigned to f. (But, there again, that'd be confusing.)

Which version are you using?

Upload a worksheet so that we can see what you're obtaining. 

@shkarah I watched the video, as well as another by the same author, on plotting.

I would not recommend following that author's techniques for handling expressions with procedure calls which, to me, do not seem sensible and robust.

@Zeineb And why didn't you mark your Question as related to Maple 18, in the first place?

@shkarah Your definition of procedure f is not set up to handle the indexed, recursive call. And so your code has a nonsensical syntax, in my opinion.

You are using the name f for function calls in two different ways, and not set up by you to resolve the discrepancy.

Why don't you state in words precisely what you're trying to accomplish?

Upload and attach your actual document.

Where is x, in your definition of f?

@permanoon123 

In general you should not be trying to use ApproximateInt from the Student:-Calculus1 package to do general numeric integration. That command provides simple and basic approaches, provided mostly as a means of introductory instruction in the topic for undergraduate students.

Much more sophisticated and powerful techniques are available using the syntax evalf(Int(....)). See this comment for some description of the basic syntax. Or see the Help system.

Of course that's not going to help get you a finite result if your integral is divergent.