Alias perhaps comes closest to "doing it automatically".

Download alias.mw

I just removed all entries with bonds with H from the table, then made the matrix, rather than deleting rows and columns afterwards; I hope this is equivalent.

graph:=proc(t::table)
  local t2,n,A;
  t2:=remove['flatten'](x->x[1][-1]="H",t);          # remove all entries from table with string ending in "H"
  n:=max(ListTools:-Flatten([indices(t2)]));                   # find Matrix size
  A:=Matrix(n,n,t2,'shape'='symmetric');                       # table to Matrix
  LinearAlgebra:-Map(x->if x::list then x[2] else x end if,A); # keep only weights
  GraphTheory:-Graph(A);
end proc:

Download Graph.mw

I was working on this but see @Carl Love was first. Here's a slight variation.

Download partitions.mw

Some of the lambda's in vvalue were not formed with the double underline (use lprint vvalue to see this). After fixing this, simplify(...,size) executes in a reasonable time.
 

Download sol1det.mw

Hard to tell without an uploaded worksheet (use green up-arrow), but it looks like NN and MM weren't given values.

To evaluate y at a particular x value use eval (for evaluate). For example,

y:=0.1*x+0.3*x^2;
eval(y,x=2);

gives 1.4

To do a lot of them, set up y as a function (technically a procedure), and put the x values you want in a list:

y:=x->0.1*x+0.3*x^2;
xvals:=[seq(i,i=0..2,0.5)];
y~(xvals)

gives [0., 0.125, 0.400, 0.825, 1.400]

plottools:-exportplot can export .svg (should also do .tiff but I got an error message). The .svg file looks correct in CorelDraw.

Download exportplot.mw

From the ?dsolve,numeric help page "All IVP methods can be used for complex-valued IVPs with a real-valued independent variable". Not sure what it would mean for a complex independent variable - some sort of path through the complex plane would be needed.

@dharr CayleyTableGroup is another way. (CustomGroup could also be used.) - works for add and multiply

Download mod7.mw

I'm assuming you really want a group, rather than just doing arithmetic mod n. The addition case is just the CyclicGroup:

Download mod7.mw

Following @Mariusz Iwaniuk but can't get the last step.

Download summation.mw

I clicked on a pMML link (5.13.E1), which downloaded a file. I opened it in a text editor, selected all the text and copied it. In a Maple 2D input region, I pasted and it asked me if I wanted to convert MathML to 2D input, and I said yes. It looks a little strange in the input region (not as bad as here), but seems to be functionally OK.

Download PMML.mw

Perhaps you want to assume n is an integer, or even or odd, in which case the following may help. If you want to use the +/- symbol, then that is not as easily done.

Download Xn.mw

@Kitonum's method requires retyping of the variable names on the lhs. This can be avoided with assign.

Download solveEqs.mw

The ExportMatrix command can take a list of Matrices and write them to a MATLAB format file. See the help page for more details.