There are many such programs, but I highly recommend WeBWorK. The founders received the American Mathematical Society award for impact on teaching math in 2016, it is used at hundreds of institutions (primarily in the United States, but I believe not exclusively at all) and is open source. You can (I think still) pay for hosting or set it up locally, which ...
I think you only need to have this knowledge if you are teaching a unit or significant part of the course, using a CAS. This is probably a small minority of courses.* In that case, what makes sense is whatever CAS you will be expecting the kids to use (I recommend picking one specific one).
The one I know is Maple, but I'm sure the others are fine too. ...
Just one small thing to consider for you:
If you like to do non-standardized exercises (i.e. the ones where the solution isn't available in a textbook), then a software can help a lot with that.
The example I like the most is the calculation of Eigenvalues. For an exercise, you usually want nice Eigenvalues (e.g. $1,2,3,4$), but how do you get an ...
The math videos creator 3blue1brown has a webpage and in the FAQ section he goes into detail about how we went about creating his videos. Here's his answer for the question "What do you use to animate your videos?"
I create most of the animations programmatically, using a python
library named "manim" that I've been building up. I’ve also used
I have not personally made videos, although I have used Maple (not free) to create many visualizations and Inkscape (free) for some diagrams. I usually prefer to write mathematics by hand, but from time to time I have used PowerPoint for slides when many visuals are required that would be difficult or time-consuming to draw by hand.
I am impressed by the ...
You could try VPython (https://vpython.org/). It's free and does 3D animation. It was built for teaching physics, and can visualize vector fields, graphs, various primitive objects, etc. as well as animating them, and letting you interact with them.
There are many good options for the "presentation" one. If you are doing multivariate calc stuff, then CalcPlot3D is a great option. (I also recommend many others such as Sage Math, which created this amazing graphic using Tachyon for image production, but CP3D is the easiest to start with.)
Perhaps what he needs (or needed) to finish his courses
is a screen-reader that can handle mathematics?
The answer to this question, Are there screen readers that can read math equations?, is Yes: There are screen-readers that can handle
MathML. They rely on MathPlayer,
"a universal math reader that now enables math to be spoken in assistive technology ...
I don't think that learning a CAS is in the category of "must-do", but it certainly is useful. Personally I use Sage but Mathematica is also a good choice. Mathematica is highly polished and widely used while sage is open source, based on a general purpose programming language, and free of charge.
I don't find myself fielding random integral questions very ...
Not an answer; just a tangential remark.
In general it is not an easy problem to reconstruct a
polygon from various sets of data. If the data does not
uniquely determine the polygon, it would not be easy
to "generate a credible figure," to quote the OP, compatible
with the partial reconstruction.
For example, the paper below reconstructs a polygon from its ...