@ So far, this looks fairly easy, and the function F is not very complicated, but there are two problems:

1. I assume that by ln, you mean the natural logarithm. The problem is that you've used is as if it were a variable rather than a function. Each use of ln needs to be followed by parentheses that enclose its argument. I can't figure out where they're supposed to go. For example, consider the subexpression ln*rho*(1-s). Do you mean ln(rho*(1-s)) or ln(rho)*(1-s)? Please correct each usage of ln and resubmit F.
2. Why have you given a numeric value to s when the goal is to find s?

Unrelated tip: The ASCII keyboard symbol for "less than or equal to" is <=. This is very widely recognized by both human readers and computer languages. Likewise "greater than or equal to" is >=. In Maple, "does not equal" is <>. This one is not as widely recognized as the first two.

1. Are x, r, and T fixed numeric values? 
2. Is F relatively well behaved (differentiable in some neighborhood of the solution)? If not, is it at least continuous in some neighborhood of the solution?
3. Is it guaranteed that a solution exists, and is it unique?
4. Can F be specified as a single expression, however complicated, or is F specified by a numeric procedure? 
5. Can you provide a Maple program for F, whether it be an expression or a procedure?

@acer Do you see any significance to the .lib vs .mla issue? In my initial reading of the Question (which was possibly based on a slightly different earlier wording), a distinction seemed to be made between having the stated problem with .lib files (or one particular ,lib file) and not having it with .mla files. I'm very unsure about that; it may have been simply my misinterpretation of the Question.

@emendes Great. I was unsure about that. Since you've now confirmed that it works, I've converted my Reply to an Answer.

To MaplePrimes administrators: I wanted to add "Maple Cloud" to the product specifications of this Question, but I see that that's not an option.

@vv That must be what the OP was referring to. I withdraw my comment about the behavior being the opposite of what was said.

I edited your Post such that now it is possible to click on the URL for the YouTube video. This is done by using the tool that looks like two links of chain on the editor toolbar.

I suggest that you change the title of this Post to reflect the mathematical and Maple-related content of your video. A title reflecting minutiae related to posting is likely to be overlooked.

@mapleatha If you construct a sum of n terms, and 1 of those terms automatically simplifies to 0, then the sum will have n-1 operands. If two of those terms cancel each other, then it will have n-2 operands. In either case, if the final result has only 1 term, then the meaning of "operand" as used by op changes. In other words, when terms become 0, they "leave no trace".

It is for reasons such as those that last week I told you that your usage of op to deconstruct differential operators expressed as polynomials in D was "very cruddy and prone to error." I meant nothing personal by that, and I wouldn't expect you or anyone to have known that already. In addition to the problems mentioned in the first paragraph, that particular usage of op had numerous other potential errors. IMO, these problems are beyond any possibility of repair; two-argument op applied to sums simply shouldn't be used for these purposes. I said that you mustn't do this or ask about it again because it'd be an utter waste of your time to try to fix something that can't be fixed. But if you want to discuss alternative methods for working with polynomials or differential operators, that's fine.

I made your question to acer regarding deleting bad characters from worksheets into a separate Question thread. It was not related to the subject of this thread. Threads are organized by the subject, not by the names of the correspondents. In other words, this is not a "chat room".

@nm My comment was directed at the OP, not at you. If it had been directed at you, it would've started with @nm . I agree with what you said about series.

@Thomas Dean You (as well as isolve) are interpretting "solution" to mean any 4-tuple (a, m, n, x) of integers that satisfy the equation. It's obvious that given any integers a and x with a <> x we can find a 1-dimensional infinite family of pairs of integers (m, n) such that (a, m, n, x) satisfy the equation. However, that's not what the OP means by "solution". By "solutions" they mean the values of x alone. Given any (a, m, n) with a <> 0, the resulting equation is quartic in x. The OP wants to know if that quartic has 4 integer solutions for x.

@greatpet The behavior of series is exactly the opposite of what you say. The order argument does specify (one more than) the maximum power. It does not specify the number of terms.

@tomleslie Vote up.

If someone wants an alternative with much less typing, at the expense of slightly more-complicated code, do this:

(f, g, h):= (0.5*x, sqrt(0.81-(x-2)^2), sqrt(3.57^2-(x-8)^2));
plots:-display(
    Student:-Calculus1:-SurfaceOfRevolution~([f,g,h], x= 0..10, output= plot),
    transparency= 0.5, scaling= constrained, color= [red, green, blue],
    caption= `` 
);

@nm On the help page ?rtable_indexing, in the section "Selecting Elements: Extracting Subblocks", the 4th paragraph is

• The result of subselection A(i1, i2,  .. , iN) on an N-dimensional array is not the same as the indexing with square brackets.  In this case, the number of dimensions of the result will correspond to the location of the last non-singleton index.  That is, if the ith index is the last non-integer index then the result will have i dimensions.

I think that this completely addresses the Question at hand. However, why this design decision was made is another matter.

@AHSAN In that case you use

for n from 20 to 30

I don't think that you understand what "default" means. It means a value that will be used if and only if no other value is given. If a value is given, it takes precedence over a default. 

@AHSAN 

The from clause of a do loop is optional and defaults to from 1. Indeed, all clauses of a do loop are optional (for, from, by, to, in, while, until).