@vv For an example of the former,

shake(sec(x));

   INTERVAL(-infinity .. -1,1 .. infinity)

So, shake implicity assumes that variables are real, which seems reasonable to me.

I haven't yet a meaningful example for INTERVAL(x, a..b), but it does seem very easy to generate nonsense with shake, evalr, and INTERVAL. Also, don't trust any prettyprinted output of these command; always examine with lprint. 
 

@Kitonum It is easy to avoid the need to enumerate or index the solutions:

seq(eval(f, s), s= Sol)

@dcatalanoferraioli Thank you. While you were typing the above Reply, I added two paragraphs to my Answer plus significant details about the composed operator. So, be sure to read those.

I am often asked about references that can help one learn Maple, but I haven't read any formal third-party references. All my knowledge comes from, roughly,

• 90% practice, experimentation (always pushing the boundaries of what the syntax will allow), reading the endogenous help files (including the Programming Guide, which is a book-length document available in-program through ?ProgrammingGuide), reading the code of Maple itself, and writing my findings here on MaplePrimes (which forces me to clearly organize my learnings in my mind);
• 9% reading other experts on here MaplePrimes, and earlier forums (both of which used to contain a much higher percentage of higher-quality material);
• 1% private discussions with programmers who work for Maplesoft.

I merged your two recent Questions. Please do not post multiple copies of essentially the same question. It's great to add additional details, but please do it by editing the original Question rather than by posting a new one. If you need assistance with editing, please ask. (Asking Questions that are only about MaplePrimes and not about Maple is fine.)

@mmcdara What you say is true, but I strongly advise the OP against wanting to do that, as I find it pedagogically unsound. In other words, there isn't much practical that can be learned by doing that or even by doing the computation in exact arithmetic at all.

@mmcdara You made at least two errors as far as I can tell:

• You didn't multiply the transformed integrand by the absolute value of the determinant of the jacobian of the transformation.
• You've exchanged the usual roles of sin(phi) and cos(phi) in your transformation. I suppose that this wouldn't matter if the integration range was also changed to phi= -Pi/2..Pi/2 rather than phi= 0..Pi.

When you finally do get the menu, in what language are its entries written? I wonder if language conversion has something to do with the slowness.

@sand15 Would you please define "bow" as you've used this word above?

If you get an error message when you try to upload a worksheet, ignore it and proceed to post anyway. Often, the error only relates to the display of the worksheet in MaplePrimes. Users who download the worksheet will nonetheless usually see exactly what you see once they open the worksheet in Maple.

I'll note that these are the same mysterious numbers that were reported by a user here yesterday, which another user claimed were the result of a "cracked" (or stolen) copy of Maple 2019.

@mmcdara 

Unicode non-ASCII characters do not require any special commands, which may be why you couldn't find any relevant help. They work in both worksheet and document modes; and, in my experience, they even work in command-line Maple running in a Cygwin window (a Linux emulator for Windows), but not in a "raw" Windows command window.

For example, in Wikipedia I found that the Unicode for the euro currency symbol is 20AC^[*1] (that's hexadecimal). So, in Maple I do

euro:= `€`;

Now this can be used anywhere in Maple symbols and strings, including in plots.

Nearly every character or symbol used in any human written language (including subject-specific languages like math or phonetics) has a Unicode, and I've always been able to find what I want in Wikipedia.

^[*1]You'll often see these listed with the prefix UTF+, as in UTF+20AC.
 

That's very weird. If you give a command other than sin, do you get the same value? What if you use the restart command first?

@mmcdara As far as I know, Maple can display any Unicode character without needing ImageTools.

@Konstantin@ Corruption seems unlikely. What was the result after restart? It is very common for mysterious problems to be corrected after restart.

I can't duplicate your error. Your commands work fine for me in Maple 2019. Could you try it again after a restart please?