@Markiyan Hirnyk  I opened your file and saw these pictures:

@idol050279  I opened your file and saw the following picture:

For some reason, transparency  option does not work on your computer

@idol050279  I do not understand the reasons for your problems. The codes from your previous message work for me as expected. The code from your last file shows some of the points inside the cylinder, and some of the points  outside of the cylinder. I do not know what do you want. If you increase the diameter of the cylinder, then all the points will be inside it.

@idol050279  Submit your code so that I can see what you see.

@idol050279  I use Maple 2016.2. You probably use an older version of Maple, in which rand command in the specified format does not work. Use the following code instead:

restart;
f:=r->RandomTools:-Generate(float(range=r,method=uniform)):
P1:=[seq([f(0..evalf(2*Pi)),f(0..2),f(0..3)], i=1..20)]:
P2:=map(t->[t[2]*cos(t[1]),t[2]*sin(t[1]),t[3]], P1):
A:=plottools:-cylinder([0,0,0], 2, 3, style=surface, strips=100, transparency=0.7):
B:=plots:-pointplot3d(P2, symbol=solidsphere, color=red, symbolsize=15):
plots:-display(A, B, axes=none);
 

Addition.  Of course, instead of random points, you can take some specific points or points that obey some regularity. For example, in the following example, the points go in a spiral:

restart;
P:=[seq([1.2*cos(t),1.2*sin(t),0.1*t], t=0..30,0.5)]:
A:=plottools:-cylinder([0,0,0], 2, 3, style=surface, strips=100, transparency=0.7):
B:=plots:-pointplot3d(P, symbol=solidsphere, color=red, symbolsize=15):
plots:-display(A, B, axes=none);
 

@AmirHosein Sadeghimanesh   Instead of  x  and  y  should be expressions of these parameters.

Example for 3 parameters:

plot([seq(seq([k[1]-k[2], k[1]+k[3], k[1]=0..1], k[2]=0..1,0.01), k[3]=0..1,0.01)], thickness=4, color=green);

@umar khan   I do not understand the reason for the error. I downloaded your file, ran it and it works correctly. I am attaching my worksheet (in Maple 2016.2).

plots.mw

@Carl Love   ListTools:-LengthSplit(L,n)  is a sequence not a list.

@Markiyan Hirnyk   I can not confirm your first calculation. I think that  value(Int(...))  is equivalent to int(...) .

In Maple 2016.2:

z := exp(I*t): 
f := z^(1/2)*(diff(z, t)): 
value(Int(f, t = 0 .. 2*Pi));
                                                          -4/3

I have not submitted any SCR.

@Markiyan Hirnyk 

Compare:

Matrix([seq(diff(y,[x$i]),i=0..nops(y)-1)]);
Matrix(nops(y),(i,j)->eval(diff(y[k],x$n),[k=i,n=j-1]));

@nm   Since  diff  command works with lists (as element-wise function), the same thing can be written shorter:

restart;
y:=[exp(2*x), exp(-x), x*exp(-x), x^2*exp(-x)]:
Matrix([seq(diff(y, [x$i]), i=0..nops(y)-1)]);
LinearAlgebra:-Determinant(%);

@st104290   If Maple can not find an explicit formula as in your example, then you can use tomleslie's method. It will work for a wider class of recurrence equations.

@leafgreen  In the syntax for a histogram, the frequencies are used instead of probabilities.  [2, 4$4, 6$5]  means  [2, 4, 4, 4, 4, 6, 6, 6, 6, 6]

@leafgreen 

Statistics:-Histogram([2, 4$4, 6$5], discrete = true, thickness = 25, tickmarks = [[2 = `ℏ`, 4 = `0`*`ℏ`, 6 = 2*`ℏ`], [0.1, 0.4, 0.5]], view = [0 .. 7, 0 .. 0.55], axes = normal, axesfont = [times, roman, 14], color = cyan, title = "Problem 7(b)");
 

@Derein  Just plot these data:

plot([seq([k, x[k]], k=1..30)]);