I've worked as a programmer before, but now I dedicate a lot of time to learning math, and so I have been using Maple.

I was wondering if there is some standard way that people work when they have a relatively large codebase. For example, can we define procedures in one file (like a document) and then just import them in another document?

I am reading about the difference between document and worksheet mode on the Maple website.

There is a table called "Difference between Documents and Worksheets" and one row has the following information


My question is about the operation on the left side. The impression I get from reading that is that if I just enter the equation in 2D math mode and hit enter it will solve the equation without me having to type in the command "solve". But Maple simply echoes the equation back to me when I do this in Maple 2022. What am I missing?

The following expression

returns undefined in Maple 2022.

I am not certain about if this limit exists, but shouldn't it be -infinity?

Why doesn't 

produce anything?

I guess this is some kind of tricky function since for non-integer x it seems not to correspond to a real number.

This came up for me when thinking about a sequence n(c^n), where |c|<1.

Is there some way to plot the values of a sequence? 

Is it possible to write 

as a polynomial in 

? This is a math question first of all. If it is possible, how do we do it in Maple.

For context, I am investigating a particular line of inquiry into answering this question about computation of Taylor polynomial.