If I understand correctly, you want to solve the partial differential equation diff(u(x,y,t),t)-diff(u(x,y,t),x)=z. The answer depends on an arbitrary function f__1 at the end. So if you have some boundary or initial conditions you can refine the solution.

Download pdsolve.mw

Here is one way. pointplot has options to control the shape and size of the point. display is used for combining two or more plots. Notice the with(plots) at the beginning. I'm not sure what you mean by "plotting the distance".

Download How-to-plot-distance-midpoint.mw

For numerical use (not necessarily for plotting), plottools:-rotate rotates an nx3 Array (datatype=float[8]) of points if you enclose it in a CURVES or POLYGONS call. I'm assuming the alpha, beta, gamma are the Euler angles, or closely related. (I've only actually used the other form of plottools:-rotate where you specify 2 points on the rotation axis and one angle.)

Download Euler.mw

This is the same problem as before; perhaps you did not read my response here.

The 19 equations don't have a solution in those variables. You could change variables or use a smaller set of equations, e.g.,

solve(eqs1[1 .. 14], {a[0], a[1], a[2], a[3], a[4], e[1], k[1], n[1], p[1]});

returns solutions.

Y is already used for something else.

N-soliton.mw

In eq5, you are missing a multiplication between the c and the (. Use a space, or better, a * for multiplication. Here c(...) is being interpreted an an unknown function named c, which solve doesn't know anything about.

maple_code_for_disease_equilibruim.mw

To add to @acer's answer, operators with names starting with & automatically are displayed as infix operators. (See the help page ?neutral.) So using &T instead of T will work, though it will display with the &. If you also want it to have a nice symbol output, choose one of the HTML codes that start with "&" and end with ";" (but not in the `&#...;` form; use the entity form). You are probably familiar with these. Many of the symbols on the operator palette are of this form. For example, I like to use

`⊗` := LinearAlgebra:-KroneckerProduct;

and use the palette in 2D input to easily input

On the main page for the app there is an "Attachment" link, separate from the "Download" link, which has a zip file with the library files, called "maple.hdb", "maple.ind" and "maple.lib" files, which comprise the package.

The strategy I gave earlier of converting to exp should work in general for any trig or hyperbolic trig functions.

Download Find_params.mw

In general if you don't want a formula, use add, not Sum or sum. You have sums 5 deep, so it will take some time. I get the answer in 2 minutes on my machine using add.

add.mw

Applying simplify to the output of EulerLagrange solves the apparent singularity problem - odeplot can now plot the solutions. However x is not changing with time so something is wrong with the physics.

Rolling_circle.mw

As far as I know, that can't be done directly with plot structures, as you surmised. You can convert to images and then manipulate as required with the ImageTools package (but maybe you figured this out already, because you did produce such an image).

Download plots.mw

Maple can find a solution to your system if given a hint. This may not be the set of solutions you are looking for. In the paper it looks like u is replaced by f,g and phi (eq 6), but you have u and f and g. So it is hard to understand the relationship of your worksheet to the paper; perhaps yoou can explain further about what you have done to get to this point. Or parhaps you like this solution.

Download PDEs_system_solution.mw

I played aound with the record form. It is nice to look at (similar to Display(dec,R) on the default output), but hard to extract the pieces. The pieces from the piecewise output can be extracted as follows.

Download Output_of_RegularChains.mw