It is impossible to understand from OP's code whether he is trying to calculate the gradient of the function of two variables (this is a vector) or the mixed partial derivative with respect to variables  x1  and   x2  (this is a scalar). In both cases there is no need to call any packages (it will be shorter and faster).

restart;
x:=<x1,x2>:
W:=<<w11, w12>|<w21, w22>>;
Cal:=(W.x)^%T.(W.x);
<seq(diff(Cal,t),t=x)>;  # Gradient
diff(Cal,x1,x2); # Partial derivative 

I propose a different approach to the solution. First we select  6  different integers (I chose numbers in the range  1 .. 10 ), and then we solve the corresponding system (here I took  t=1). as it was done in your previous post for numbers  1 .. 6 . Thus,  71  solutions have been found that satisfy all your conditions. Unfortunately, the code runs rather slowly (it took about 45 minutes), because Maple takes about 11 seconds to solve one system. As an example, the graph of  f(x)  is plotted for one solution.
 

Download intsol.mw

If you still want to use the standard notation  |v|  for the Euclidean length of the vector  v , then first run this code (VectorCalculus package is not needed). Using code in  2Dmath  only:

Download v1.mw

 Pascal4QM  you wrote  "...difficult to generilize to an arbitrary number of nested sums."

Here are 2 procedures for working with nested sums of arbitrary nesting order. The first procedure allows you to automatically generate a nested sum of any nesting order. The second procedure changes the summation order for an existing nested sum.

Download Nested_Sum1.mw

A:=Sum(Sum(f[n]*g[q-n]*exp(2*I*Pi*q*x),q = -infinity .. infinity),n = -infinity ..infinity);
Sum(Sum(op([1,1],A),op(2,A)),op([1,2],A));

                                     

The imaginary unit in Maple is coded as  I , not as i.

You have already been answered that  Optimization:-Minimize does not solve the problem. But if you are looking for software that does this, then try the  DirectSearch  package. It is not part of the Maple library and must be loaded from  Maple Application Center. See
https://www.maplesoft.com/applications/view.aspx?SID=101333

Example of work:
 

Download DS.mw

for c from 1 to 10 do
p||c := plot( x^c, x= -1..1, title= typeset("The power is  ", c) )
end do:
p3;

Edit. As acer showed your problem can be solved in many other ways. But if it is necessary to combine text and more complex math, then I do not know any other simple way than using  typeset . See the example:

f:=cos(3*x)/(x^2+1):
plot(f, x= -4..4, title= typeset("The plot of the function  ", y= f), titlefont=[times,bold,16], scaling=constrained, size=[800,300] );

See help for details  ?plot,typesetting

I think the problem with your calculation is that the function  cot(x)  is infinity  if  x=Pi*k , k is integer. But if the integration range does not contain these points, then the integral can be calculated as below:

restart;
U:=(x,z)->-1/(x^2+a^2)*cos(x)*(cos(sqrt(x^2*(x^2+1)/(x^2+2))*z)-cot(sqrt(x^2*(x^2+1)/(x^2+2))*L)*sin(sqrt(x^2*(x^2+1)/(x^2+2))*z));
L:=10: a:=1:
V:=(X,Z)->evalf(Int(U(x,z),[x=0.1..X,z=0.1..Z]));
plot3d(V,0.1..0.4, 0.1..0.4);

Download doubleint.mw

Maple has a huge number of specialized packages, and it is not always easy for a beginner (and often an experienced user) to find the right command and understand all of its options. Fortunately, the same problem can be solved by various methods. If we are talking about plotting some kind of graphic objects, then in addition to the commands of the kernal (plot  and  plot3d), it is very important to master the main commands from the packages  plots  and  plottools . When working with lists, the  ListTools  package is very often used. Below your problem is solved using these packages without the  Statistics  package. This should work on any version of Maple.

L := [1,2,2,2,3,3,4,4,5,5,6,6]:
n:=nops(L);
L1:=ListTools:-Collect(L); m:=nops(L1);
S:=seq(plottools:-rectangle([i-1/2,L1[i,2]/n],[i+1/2,0],color="LightBlue"),i=1..m):
plots:-display(S, view=[0..m+1,0..0.3]);

This method allows you to easily diversify the shape of graphic objects. For example, instead of rectangles, it is easy to plot triangles or other shapes.

S1:=seq(plottools:-polygon([[i-1/2,0],[i,L1[i,2]/n],[i+1/2,0]],color="LightBlue"),i=1..m):
plots:-display(S1, view=[0..m+1,0..0.3]);

 
Histograms.mw          

Everything seems to be working properly (or you expect other answers):

restart;
L:= [1,2,3,4,5,6,7,8];
Statistics:-Quartile(L,1);
Statistics:-Quartile(L,2);
Statistics:-Quartile(L,3);

                                L := [1, 2, 3, 4, 5, 6, 7, 8]
                                2.4166666666666666666
                                4.4999999999999999999
                                6.5833333333333333333

B:=N->Matrix(N+1, {seq((i,i+1)=i, i=1..N)});

Example of use:
B(5);

restart:
x := 12:
y := 46:
s := 0;
'x' = x:
'y' = y:
'`résultat`' = s: k:=0:
while 0 < y do
if type(y, odd) then s := s + x:
y := y - 1:
else x := 2*x:
y := y/2:
end if;
k:=k+1; L[k] := [x, y, s];
end do;

op~(convert(L,list));

Example of use:

combinat:-partition(4);
             [[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4]]

You may be interested in this post  https://www.mapleprimes.com/users/Kitonum/posts?page=6

If you add one more parameter (I added  m ), Maple will find a huge number of solutions. Below is found and built the plot for one solution:

Download Equation.mw

Yes, I can confirm that the legend option does not work (I checked in Maple 2018.2). In a sense, this is natural, because legend option is associated with the image of curves, rather than regions. Use  caption  instead, as in the example below:

plots:-inequal(x^2+y^2<=1, x = -1.2..1.2,y=-1.2..1.2, caption = typeset("A region of  ", x^2+y^2<=1, "."), captionfont=[times,bold,16], scaling=constrained);

You can put this text anywhere on the screen. See  ?plot,typesetting

If you need to put legends for curves, you can do as below:

A:=plots:-inequal(x^2+y^2<=1, x = -1.2..1.2,y=-1.2..1.2, color=pink, title = typeset("A region of  ", x^2+y^2<=1, "."), titlefont=[times,bold,18], scaling=constrained):
B:=plots:-implicitplot(x^2+y^2=1, x = -1.2..1.2,y=-1.2..1.2, color=red, thickness=3, legend = typeset("A curve of  ", x^2+y^2=1, "."), legendstyle=[font=[times,14]]):
plots:-display(A,B);