Of course this is inferior in its capabilities to acer's method, but it is simpler:

Download textplot.mw

solve~(5*x=~[5, 20, 50] );

                               [1, 4, 10]

restart;
m1 := Matrix([[1, 2], [3, 4]]);
m2 := Matrix([[5, 6], [7, 8]]);
'm1'.'m2' = m1.m2;
#  or
'm1'*'m2' = m1.m2;
# or
InertForm:-Parse("m1*m2"):
InertForm:-Typeset(%)=m1.m2;

Edit.

See wiki  https://en.wikipedia.org/wiki/Music_and_mathematics

See:

l := t -> 0.5*tanh(0.5*t):
deq := diff(f(t), t)*l(t)*(diff(f(t), t, t)*l(t)+9.8*sin(f(t)))+diff(l(t), t)*(diff(f(t), t)^2*l(t)-9.8*cos(f(t))+4*(l(t)-0.5)) = 0:
eval(deq, t=0);
eval(%, f(0)=0);

                             -0.500 - 2.450 cos(f(0)) = 0
                                         -2.950 = 0

This is a well-known method. I made a cut for better visibility and chose the same scale on the axes:

f:=r->exp(-(r-3)^2*cos(4*(r-3)));
plot3d([r*cos(phi), r*sin(phi), f(r)], r=1..5, phi=Pi/3..2*Pi, scaling=constrained, axes=normal);

Above is the rotation around y-axis (y-xis pointing upwards).

Addition. Rotation around x-axis (with a cut):

restart;
f:=r->exp(-(r-3)^2*cos(4*(r-3)));
plot3d([r,f(r)*cos(phi),f(r)*sin(phi)], r=1..5, phi=Pi/2..2*Pi, style=surface, scaling=constrained, axes=normal);

Animation the rotation around x-axis:

restart;
f:=r->exp(-(r-3)^2*cos(4*(r-3)));
plots:-animate(plot3d,[[r,f(r)*cos(phi),f(r)*sin(phi)], r=1..5,phi=0..a, scaling=constrained, axes=normal], a=0..2*Pi, frames=90);

rotations.mw

You use the same name  B  to create different objects. List B is not used at all in the code.

Corrected code:

restart;
interface(rtablesize=50);
E:=[E1,E2,E3]:
P:=[0,1,2]:
N:=3:
for b from 1 to 12 by 5 do
F:=(i,j)->
if i=b+P[a] and j=b+P[a] then E[a]
elif i=b+P[a] and j=b+N+2+P[a] then -E[a]
elif i=b+P[a]+N+2 and j=b+P[a] then -E[a]
elif i=b+P[a]+N+2 and j=b+P[a]+N+2 then E[a]
else 0:
end if:
B[b]:=add(i,i=[seq(Matrix(20,F), a=1..3)]);
end do;
H:=[seq(B[b],b=1..12,5)];

Use  seq  command for this:

v := Vector[row]([seq(4*n, n = 1 .. 6)]);

The code will be quite simple if you do not draw a vertical line. It is also easy to depict the curve and the region in different colors:

plots:-display(
   plot(1/ra, x= 0..0.5, 0..10, color=yellow, filled),
   plot(1/ra, x= 0..1, 0..10, color=blue, thickness=2));

I think it will be easier to immediately specify  F  as a function:

F:=(x,y)->f(x)+g(y);
F(x,x);

View -> Show/Hide Contents 

Remove the tick from the "input"

Unfortunately Maple unlike Mathematica weakly solves the problems of an optimization symbolically (exactly). Here are two simple examples:

maximize(x^2+y^2, x=0..1, y=1);  # OK for rectangle region
maximize(x^2+y^2, x=0..1, y=1-x);  # Maple fails for triangular region

This example  z=(1-y^2)/(x^2), x^2 + y^2 <= 1, x>=1/2  is easily solved without Maple by hand. Consider cross-sections of the surface by planes  x=C, where  C  is constants. We have z=(1-y^2)/(C^2)=1/C^2 - 1/C^2*y^2 .  These curves are parabolas (branches down) with vertices at points  (C, 0, 1/C^2) . As  C  is increased, the vertices goes down, so the  maximum is 4  and it reached at the point  x=1/2, y=0 .

Visualization:

plots:-display(seq(plots:-spacecurve([x,y,(1-y^2)/(x^2)],y=-sqrt(1-x^2)..sqrt(1-x^2), color=red, labels=["x","y","z"]),x=0.5..1,0.05));

You have an equation with 3 parameters. If you specify the values of these parameters, it is easy to find all the roots.

Example:

Download mm_new.mw

All the real solutions of this equation are clearly visible on the plot (in particular, we see for u>0 and v>0 not one but an infinite number of solutions - two branches of solutions from points  (1,0)  and  (0,1)  and going to infinity) . It is possible to obtain explicit equations for these branches if we solve the equation with respect to one variable:

plots:-implicitplot(1/(u+v)^2+4*u*v-1=0, u=-3..3, v=-3..3, size=[500,500], gridrefine=5);

Sol:=solve(1/(u+v)^2+4*u*v-1=0, v);
plot(Sol[1], u=1..5);
 

Example:

A:=plot(sin(x), x=-1..4*Pi+3, color=red, thickness=2, labels=["",""]):
B:=plots:-arrow([0,-1],[0,2.2], shape=arrow,head_width=0.7,head_length=0.12):
C:=plots:-arrow([-1,0],[4*Pi+4,0], shape=arrow,head_width=0.1,head_length=0.9):
T:=plots:-textplot([[4*Pi+3,-0.1,x],[-0.9,1.1,y]], font=[times,roman,18]):
plots:-display(A,B,C,T);