@Stretto The underscore character is not an operator---it's treated like a letter of the alphabet---and it can't be overloaded. But you can define an operator &_, and you wouldn't even need to overload it because it has no predefined meaning:

`&_`:= q:

Now x &_ n returns q(x,n). Note that a space is needed after the underscore; the space before the & is optional.

@tomleslie Your solutions happens to satisfy the 0..1 constraints, but it seems like just luck that it does so.

@shkarah I watched parts of the video. Parts of it move too fast to understand, and parts of it move too slow to bear watching. Anyway, I agree that you've been led astray by it, and I don't know why it works in the video.  Is it possible to get the worksheet from the video's maker?

I concur with Acer and Christian. After the value of f(x) has been assigned, any references to f[i] are suspect and risky. Sometimes it works, but is it worth the effort to debug if it doesn't? Just use another name instead. 

I haven't investigated this case; I just formed an opinion from reading your code.

@permanoon123 Still, it's not possible to get an answer without knowing the function f.

@student_md 

Firstly, you should post your worksheet inline so that I can read it in any browser, such as on my phone.

Secondly, getting decimal results is premature at this point. Let's first make sure that the symbolic results are correct. 

Thirdly, the two iquo commands that you mentioned are equal: iquo is the integer quotient, and m is precisely the discarded remainder.

@acer This is just curiousity because I'm unlikely to use labels, but can they only be used with explicitly displayed output? Nonetheless, I think that the answer to this will be of interest to the general reader. 

@syhue Ordinary characters in strings---commonly called bytes---occupy 8 bits. The command convert(P, 'bytes'), where P is a string, returns a list of numbers from 0 to 255, one number for each character. Thus, this list can be thought of as a number in base-256 = 2^8. 

The operation m &^ e mod n takes essentially the same amount of time regardless of whether m is large or small; thus, for efficiency, we want each number m that is encrypted to represent as many message characters as possible (which I called a "chunk" of characters). On the other hand, in order to guarantee uniqueness of represention, in other words to guarantee that
((m &^ e) &^ d mod n) = m for all m, it's necessary that m < n. What I called bch is 1 more than the maximum m that I allow. Since it's inconvenient to split individual characters, I make bch a power of 256. So 
bch = 256^"number of characters that can fit". The number of characters that can fit is 
​​​​​floor("bits in n" / "bits per character"). In efficient Maple syntax, that's 
iquo(ilog2(n), ilog2(bby)).

Now, hopefully you can see that this bch is the numeric base of the list M. The Maple command to convert a list L representing a number in base A to a list representing the number in base B is
convert(L, 'base', A, B). (It's possible to make this step more efficient by making use of the fact that B is a power of A.)

Do you understand?

I think that you should vote up my Answers by clicking on the thumb icon.

@Mac Dude You misunderstand my point entirely. I was commenting on your continuing the OP's use of f^4; I was not commenting on your use of f@@4 without arguments. Indeed, my Reply was added before you had edited your Reply to use @@ at all. In other words, I was the first person in this thread to make any reference to the @@  operator, and I did so merely to make readers aware of its existence as the proper Maple operator to use for what was up until my intervention being refered to as f^4.

I have no problem with using f@@4 without arguments to refer to the fourth-order self composition. And if you do include arguments, it must be (f@@4)(x,y), not f@@4(x,y).

Please post an example of the phenomenon that you describe, either as plaintext or a Maple worksheet.

@Norwegian explorer You have two procedures named i. So, the first one is never used and never could be used. 

Also, the second procedure i uses i as a local variable. This is not a problem, but it's a bit unusual.

Your weight function omega is not strictly real-valued for x in [0,1]. Isn't that a problem?

I think that this one takes the cake as the most irrelevant Maple error message that I've ever seen. 

@Mac Dude To avoid abusing the notation, the Maple syntax for the object under discussion is (f@@4)(x,y).

@syhue It is not biased.

The thing that I was saying is biased is

nextprime(rand(...)())