@Bendesarts 

The error message in your picture is too small to read. Would you please type it in? I think that it says that the package does not contain an angular_velocity command. The results of the with command indicate that show is the only command in the package.

Your Question contains no text and no attached file.

@Bendesarts 

There is no source code stored in the .mla file; you'll have to use a method like mine with those. If the package is claimed to be "open source", then there should be a source-code file with the package---either a plaintext file or a worksheet.

@sercan 

I haven't been able to prove the inequality with Maple or otherwise. Is this an exercise, i.e., do you know that a proof exists and you just have to find it? Or is this original research?

Please provide the p, q, e, and d for which it doesn't work.

The procedure only works for b < N. Is that the case? For b >= N, you need to divide the plaintext into smaller chunks.

@Preben Alsholm 

A great substitution; I didn't know that IntegrationTools:-Change could make use of assumptions. Vote up. In some versions of Maple (notably Maple 16), an expand may be required before the eval to force the y outside the integral to cancel with the y in the denominator of the integrand.

If Gamma is entered as the exact value 1/5 rather than 0.2, you can use value on the integral and prove that it is exactly 1.

@ecterrab 

If you are using 1D input, there is a preliminary step needed before you can use Edgardo's Answer. Highlight the expression, right click, and Convert To -> 2D Math Input. Then follow Edgardo's instructions.

@hazif firas 

Sorry, I can't solve your problem. I got past the "initial Newton..." error, but then I get a division by zero.

I just want to point out that Runge Kutta Fehlberg 4 5 (rkf45) is a method for IVPs, not BVPs. There is no way to tell Maple to solve a BVP with rkf45.

I haven't looked at your worksheet yet (I will). But I want to point out that undefined and Float(undefined) are not errors; they are mathematically valid answers. For example limit(1/x, x= 0) is undefined.

@sercan 

Can you supply ranges for the constants and variables? For example, are any of them guaranteed to be positive? Are there also relations such as w > c that hold? Maple can often prove an inequality when given some assumptions on the variables.

By "better", I assume that you mean ProfitB >= ProfitC for all values of the variables and and constants. Is that right? Then there's really no distinction between variables and constants.

[I edited your Question due to excessive whitespace.]

I doubt that there's any simplification for that. Just looking at n=2, I see no simplification. Are you sure that you want a summation rather than a product? If you change Sigma to PI (Maple command product) then there's a simplification.

Is the issue that you want to prove that the functions are identical?

How about posting your Maple code with the functions?

@Kitonum 

Change 3 to length(j).

@nm 

There is nothing wrong with having text or any other data structure in a matrix. Indeed, certain commands in Maple require an Array, Matrix, or Vector of plots. I understand your point about "lists of lists," but note that a Maple Matrix is different from a Maple list of lists.

There is nothing wrong with having keys in a set.

@mzaman