You can have several worksheets open with the same Maple engine - See Tools->Options->General tab, and under Mathematical Engine choose "Share one engine among all documents".

Alternatively you can save variables with the save command, and then use the read command to retrieve them.

Download tobase.mw

In general there are many roots. An implicitplot will show curves where there are solutions. The algcurves packsge has more routines to analyse such curves.

Download bivariate.mw

Here I use @acer's routine and color the digits according to HUE: 0..1 maps to 0..16777215.
Don't know how to do the more general case with non-integer bases.

[Edit: forgot the decimal point - now fixed]

Download expcolors.mw

ctrl-k inserts a new execution group before the current one; ctrl-j after the current one (cmd-j,cmd-k on Mac). There is also the >_ icon on the toolbar that inserts after the current execution group. I'm assuming worksheet mode; for document mode to get new input but not a new prompt it is ctrl-shift-k etc.

You could use string manipulations to automate a file conversion for the simple stuff as in the example file below, and then hand edit the file for the things that don't easily convert. (integrate is a synonym for int, so you could leave that). Of course you could spend a lot of time on a more sophisticated conversion process, but I'm guessing it is easier to do an approximate conversion and then fix things up in Maple. I "read" the modified file in the example, which means that Maple parses the commands, but it might be easier to copy from the converted file to an input region.

MaxToMaple.mw

Spelling error

wiht(LinearAlgebra) should be with(LinearAlgebra)

There is no general formula in terms of radicals for a general 5th degree polynomial. For some cases of coefficients there will be solutions, roots(x^5-1); is a simple example.

As @Carl Love says, walks are enumerated by the adjacency matrix, and can be used to do this.

Download Walks3.mw

I think this is fairly robust.

get_exponent:=(expr,x::name)->diff(expr,x)/expr*x:

get_exponent(x^2,x);
get_exponent(x^(n-1),x);
get_exponent(3*x^(n+2),x);
get_exponent(3*x[2]^k*x[3]^(n+2),x[3]);

    
                               2

                             n - 1

                             n + 2

                             n + 2

Once you entered floating point values in your Matrix, the implication is that you have given up on symbolic solutions. Since the Matrix wasn't obviously of a structure that has real eigenvalues, the algorithm used was a general one that generated complex values. As @acer pointed out, you can then make them look nicer, but the algorithm used is the same. For a symmetric Matrix, if you use shape=symmetric, then Maple will choose an algorithm that will produce real eigenvalues and eigenvectors (try it on A:=Matrix(2,2,[[0.8,0.3],[0.3,0.7]],shape=symmetric);).

But if you enter exact values in the first place, then Maple will do the whole calculation exactly. In general, this is the power of Maple over a regular programming language. Here I converted the values you entered to rationals to avoid re-entering, but you could have entered these directly.

Download Eigenvectors.mw

Yes, my Maple 2023.0 on Windows 10 shows this behaviour.

Try Insert->Table and choose 1 row, 1 column, Title: "Fig. 1" and tick Show caption. Then Insert->Image->From file and choose the file. After you have it, right-click (cmd-click on Mac) and choose Table -> Properties, Table size 50% and the image will reduce size 50% keeping the aspect ratio. That menu also has a "Caption" tab which gives several ways to specify the caption. As far as I know there isn't automatic renumbering.

(As you probably already found, you can insert images in a text area but resizing with the handles doesn't maintain the aspect ratio.)

(Notice that _B2 stands for a binary variable with values 0 or 1, but _Z1 and _Z2 are (different) integers.)

Download underline.mw

Your code has a list M := [0, 0.5, 1.0, 1.5, 5] which you insert into other expressions as though it were a single number. So even for F[3] that isn't sensible. This ultimately leads to the error message.