f := diff(a*y*sin(b*x + c), x,y): h := x -> unapply( f, a,b,c):
h(x);
               (a, b, c) -> a b cos(b x + c)

Now you can play with different values of a,b,c:
h(x)(3,4,5);
                        12 cos(4 x + 5)

plot(k, w = 0 .. 15, color = ["OrangeRed"], labels = ["w", "Determinant"]); p:= %:
PlotData := plottools:-getdata(p)[3];

(1) If n integer, then a^n is evaluated as 

`*`(a$n)

whatever the value of a. So 0.0^0 gives 1 (empty product)

(2) if b is a float, then a^b is evaluated as

exp(b*log(a)), where exp(-Float(infinity)) = 0.0

So

0^0.0;
                        Float(undefined)

Int is the inert form, and int the active form. If f is not defined, then the active form is unevaluated:

The ranges of x- and y-values can be obtained by

p := plot(x*sin(x), x=0..Pi):
plottools:-getdata(p)[2];
     [0. .. 3.14159265044999980, 0. .. 1.81963128310659839]

eq1:=x^2-y^2=a*z^2:
eq2:=x-y=a*z:
simplify(eq1/eq2);

(note that your answer is wrong)

It is not clear what rectangle you want to plot. For example, if you know the edges:

plots:-pointplot3d( [[0,0,0],[1,1,0],[1,1,1],[0,0,1],[0,0,0]], connect=true, color=black, axes=normal );

f:=x->x^2 -3*x + 2; D(f)(x);

i.e: ":=" instead of ":"

"3*x" instead of "3x"

";" (or ":") instead of ","

You forgot a multiplication sign: 3*(2*x-1)*(x+1) > 0;

There ara many, many roots. If I set view=-1..1 in the plot command, I get

and, for example:

Digits := 30: G[0] := 0:
for k to 4 while G[k-1]<10000 do        
G[k]:= RootFinding:-NextZero(K, G[k-1], maxdistance= 10000, guardDigits= 3)  od;
              0.000593466734563716148722323594000
               0.00755337183456371614872232359400
               0.0292055307345637161487223235940
              -0.000788904965436283851277676405000

num_n := dsolve({c_i1, c_i2, Ecuacion_1, Ecuacion_2}, numeric, method = classical[rk4], {u(x), v(x)}, stepsize = .1, output=listprocedure);

U := subs( num_n, u(x) );

I think that Maple hasn't paid much attention to the LaTeX export possibility for the last versions. And even before, rather much finetuning by hand was needed, e.g. breaking large formulas over several lunes, spacing, etc.

Also 2D-Math input doesn't work very well, so use Maple Input instead.

BTW: you can upload a *.tex file if you change the extension to >txt

The variable res is a list of procedures, not a table or an array. Perhaps you want to convert res to a sequence:

op(res)

But if you want to use the results, for example f₁(x):

F1 := subs( res, f1(x) ):
plot(F1, 0..1 );

or

O2 := subs( res, omega2 ):
O2(0), O2(1);
     3.973052426735284, 3.9730524267352827

W:=expand(convert(rhs(b1),polynom));

Try

evalc~(Re~(A));