For the plotting you must specify all the parameters. 

Example of the plotting:

restart;
schro := -(diff(psi(x), x, x))+(2*a*b*x^4+a^2*x^6+(b^2-a*(2*p+3))*x^2-(2*p+1)*b)*psi(x) = 0:
dsolve(schro);
assign(%):
plot(eval(psi(x), {a=1,b=1,p=1,_C1=2,_C2=1}), x=0..2);

multiply the latter matrix by 1/a^(3/4) :

A:=<a,b,c,d; e,f,g,h; i,j,k,l; m,n,o,p>;
B:=<a,b,c,d; 0,-e*b+a*f,-e*c+a*g,-e*d+a*h; 0,a*j-i*b,a*k-i*c,a*l-i*d; 0,-m*b+a*n,a*o-m*c,a*p-m*d>; 
D1:=LinearAlgebra[Determinant](A);
D2:=LinearAlgebra[Determinant](1/a^(3/4)*B);
D1-D2;

Download M.mw

plots[inequal]  command works for inequalities with 2 variables only. In your example 4 equalities with 3 variables are given. You can display them by plots[implicitplot3d]  command:

plots[implicitplot3d]([x-y-z=3, 2*x-y+2*z=5, x-y+z=1, 3*x-y-5*z=5], x=-7..7,y=-7..7,z=-7..7, color=[red,blue,green,yellow], style=surface, axes=normal,view=[-8.4..8.4,-8.4..8.4,-8.4..8.4]);

plots[inequal]  command works for inequalities with 2 variables. In your example 4 equalities with 3 variables are given. You can display them by   plots[implicitplot3d]  command:

plots[implicitplot3d]([x-y-z=3, 2*x-y+2*z=5, x-y+z=1, 3*x-y-5*z=5], x=-7..7,y=-7..7,z=-7..7, color=[red,blue,green,yellow], style=surface, axes=normal,view=[-8.4..8.4,-8.4..8.4,-8.4..8.4]);

Inequality  A>B  is equivalent to the inequality  A-B>0  and it will be true if

Optimization[Minimize](A-B, {constraints})[1] > 0

Examples:

A := 2*x^2+(y-2)^2-1: 
B := x^2:
Optimization[Minimize](A-B);  # On the whole plane (x,y) the inequality  A>B  does not hold 
Optimization[Minimize](A-B, {2*y <= x});  # At a given halfplane   2*y <= x  the inequality  A>B holds
is(%[1]>0);

Another way:

type(390/7, integer);

                                   false

I took  x0=0, y0=1 .

restart;
x0:=0: y0:=1:
plot([(-y0 - x0)*exp(-2*t) + (y0 + 2*x0)*exp(-t),  -2*(-y0 - x0)*exp(-2*t) - (y0 + 2*x0)*exp(-t), t=0..10], labels=[x,y]);

X:=(1/6)*sqrt(2)*sqrt(sqrt(13)+11):  Y:=-1/6+(1/6)*sqrt(13):
x:=y->piecewise(y<=1 and y>=Y, X/(Y-1)*(y-1), y<Y and y>=-Y, X, X/(-Y+1)*(y+1)):
T:=plots[textplot3d]([[1.35,0,0, x, align=below],[0,1.35,0, y, align=below],[0,0,1.15, z, align=right]], font=[times,roman,18]):
A:=plot3d([x(y)*cos(alpha), y, x(y)*sin(alpha)], y=-1..1, alpha=0..2*Pi, style=surface, color=khaki, view=[-1.4..1.4,-1.4..1.4,-1.2..1.2], axes=normal, orientation=[15,70,0]):
plots[display](A,T);

User lighting was used.

It can be done only for solving of a linear equation by Student[Basics][LinearSolveSteps] command. See help on this command.

Example of use:

Student[Basics] [LinearSolveSteps](2*x-1=1/3+x, x);

Do not use brackets to group terms in an expression. They are only used to create lists. 

plot(9.2-8.93*35.3/(11.17-8.93)*(exp(-8.93*t)-exp(-11.17*t))-8.3*exp(-11.17*t), t=0..1);

Straight from the Maple worksheet window:

Help -> On the Web -> Application Center

and download the applications that interest you. 

Unfortunately for the problem to collect  rhs(aa)  for  omega^(-sigma+1)*L   neither  frontend  nor  freeze  method does not work. Here 2 more complicated ways to solve the problem.

First way:

lhs(aa)=applyop(collect, [1,1], frontend(collect, [rhs(aa), omega^(-sigma+1)]), L);

Second way uses  subs  and   collect  commands only:

lhs(aa)=subs(t=omega^(-sigma+1)*L,collect(subs(omega^(-sigma+1)=t/L, rhs(aa)), t));

The solution to the second problem:

lhs(aa)=applyop(factor, [1,1], frontend(collect, [rhs(aa), omega^(-sigma+1)]));

or simply

simplify(aa);

for full factorization.

restart;

r:=6:
plot3d([r*sin(theta)*cos(phi), r*sin(theta)*sin(phi), r*cos(theta)],  phi=0..2*Pi,  theta=0..Pi);

Addition: The shortest way of plotting a sphere is

restart;
plots[display](plottools[sphere]([0,0,0], 6));

Small circles at the ends of the segments should be plotted separately:

f:=x->piecewise(type((x+2)/4,integer)=false,x-floor((x+2)/4)*4, undefined):  # Setting for your function
f(2.5), f(-2), f(2), f(6);
A:=plot(f, -10..10.1, scaling=constrained, discont):
B:=plot([seq([-10+4*k,-2],k=0..4), seq([-6+4*k,2],k=0..4) ],style=point, symbol=circle):
plots[display](A, B);

f(x,y,z)=1  is a surface in the 3D-space. It can be plotted by  plots[implicitplot3d]  command.

Example:

plots[implicitplot3d](x^2+y^2-z^2=1, x=-3..3, y=-3..3, z=-3..3,  numpoints=8000);