@asa12  In my code  sols  is  a list not a vector. So try first convert your  sols[11]  into list:

convert(sols[11], list);

@asa12   My code works in Maple 12. You should just click by the mouse on the plot, and press "play " on the animation panel.
n is the number of vertices in the broken line (nops(sols)= 9), and 5 is the number of frames to display each segment. If the number of frames to increase, it will be more smooth animation.

@acer  Yes you are right,  assuming exp(2)-1>0  can be omitted. I wrote it by an analogy with sqrt(x^2) assuming x>0;

@Carl Love  You changed your style - instead of a single line of a code you write three lines.

Matrix(2,3, (i,j)->`if`(i=1,`Matrix `||j, LinearAlgebra[RandomMatrix](2)));

@RafaeldeGomes

Example:

L1:=seq(LinearAlgebra[RandomMatrix](2), i=1..5);
L2:=seq(LinearAlgebra[RandomMatrix](2), i=1..5);
L3:=seq(LinearAlgebra[RandomMatrix](2), i=1..5);
for k from 1 to 5 do
L1[k], L2[k], L3[k]
od;

@MDD  If you need to repeat a similar plotting several times, a special procedure is required for this. The planes forming facets of your polyhedral cone should be the parameters of this procedure.

I also got this message after about 15 - 20 minutes  as I posted the answer to Brian's question. Then I accidentally discovered that Brian's question mysteriously turned into a post. I would like to get an explanation of who did so.

Unfortunately I do not remember where I wrote about this formula, so I wrote again this simple procedure. The procedure returns the oriented area of a non-self-intersecting polygon:

Shoelace:=proc(L::list)
local n;
n:=nops(L); 
(1/2)*add(L[i, 1]*L[i+1, 2]-L[i, 2]*L[i+1, 1], i = 1 .. n-1);
end proc: 

Example of use:

L:=[[3, -1], [-2, 2], [5, 6], [2, 3/2], [3, -1]]:
Shoelace(L);
plots[display](plottools[polygon](L, color=yellow));

In this post  Shoelace  procedure was generalized  (Area  procedure) for a region in the plane bounded by a non-self-intersecting piecewise smooth curve.

@MDD   A, B, C  are the points of intersections of the plane  x+y+z = 1  with the original planes (I put these points on the plot). The faces of the obtained solid angle is easy to paint in any color using  color option in plots:-polygonplot3d  command. Edges also can be painted, if you use  plottools[line]  command:

restart; 
S := {-x+2*y, -x-y+3*z, 3*x-2*y-z, x+y+z = 1}: 
A, B, C:=map2(eval, [x,y,z], solve~([seq(S minus {S[i]}, i = 1 .. 3)]))[ ]; 
OO := [0, 0, 0]:
Points:=plots:-textplot3d([[A[],"A",align=below],[B[],"B", align=above],[C[],"C",align=below]], font=[times,roman,16]):  
plots:-display(Points,plots:-polygonplot3d([[OO, A, B], [OO, A, C], [OO, B, C]], color=[red,green,blue], axes = normal, labels = [x, y, z], labelfont = [times, roman, 16], orientation=[70,65,0]));

Solid_angle1.mw

@umar khan   If  L  is a list then  L[n]  is  n-th element of this list.

@Vee  Everything is fine:

evalc((-1)^(1/3));
expand(%^3);

                     1/2+(1/2*I)*sqrt(3)

                                -1

@Vliegkikker  Maple easily solves linear systems, and if it does not return any answer, it indicates that the system is inconsistent.

@rlopez  Thank you for your comment. I am familiar with this command. But I always prefer to use a command from  Maple kernel, if it solves the same problem. Also the code

plot([Re,Im]~([%]), style=point);

is a bit shorter than

plots:-complexplot(convert(V, list), style=point);

@Carl Love  Thank you for your helpful comments.

@umar khan 

1. Maple does not write a constant at indefinite integration, you can easily do it yourself.

2. For the numerical solution of a system of two equations  2 initial conditions are necessary.

3. I wrote  u(R)=0  arbitrarily, you can write your own value as you need.

4. Since you wrote "to integrate of  z(x)  from  0  to  x" , to plot I have picked up the constant  so that  u(0)=0 .