@nMaple  All surfaces in my code defined by parametric equations, in which polar coordinates  r  and  phi  was actually used.  r(z)=2+6*((z-5)*(1/5))  is the equation of the line  through the 2 points  (5,2)  and  (10,8)

@Markiyan Hirnyk  Here are the basic steps in my code:

1) First, we specify the list  Lines  of 4 lines and the set  Points1  of 22 points (2 points for each domain).

2) Next we find the set  Packs  of all 4-points subsets of  Points1.

3) Next in a for loop, we choose such  sets of  Packs  that satisfies the condition (2 points on each side of any of the four lines). We get the set  Teams .

4) Using  ListTools[Categorize]  command  we divide the  set  Teams into equivalence classes on the basis:: two elements of  Teams  belong to the same class if the points of them lie in the same domains.

5) From each class choose one (first) element. We got the final result  Confs .

@sunflower  You can not write p[i]  because it  (i - the variable of the loop)  is not the  i-th prime number.

Write a for loop with the condition  irem(n,18)=0 and irem(n,10)=0

Very strange that Maple can not do without additional options to solve this simple system, which can easily be solved manually. Perhaps this should be seen as a bug.

@want to be a permanent vegan  The only new issue in your new question - is finding the integral of the function, which occurs in the numerical solution of the system of differential equations (also the initial conditions must be present). To find the integral add to your system an additional function, using the fact that  int(f(t), t=x0..x) = g(x)  is equivalent to 2 equalities  diff(g(x),x) = f(x)  and  g(x0) = 0 

@tomleslie  The same can write shorter:

f:=x->x*cos(x)-sin(x)*sin(x/1000);
r:= 0:
to 20 do
r:=RootFinding[NextZero](f, r);
od;

@snowww  

restart;

N := {F = 1, K = 1.2}:

Eq := diff(C(x),x,x)-F*(diff(C(x),x))-F*K*C(x) = 0:

Bcs := F*D(C)(0) = C(0)-1, D(C)(1) = 0:

Sol := dsolve(eval({Bcs, Eq}, N), C(x)):

assign(%);

plot([C(x), eval(exp(-K*x), N[2])], x = 0 .. 3, 0 .. 3, color = [red, blue], thickness = 2);

@snowww  You have to love Maple and work with it constantly.

@farzane  The above code works well in this case also:

A:= .5464691235-.4473247264*I,  -.4563184747+1.*10^(-14)*I,  .5464691235+.4473247264*I, 0.9091925189:

Re(sort([A], (z1,z2)->abs(Im(z1))<abs(Im(z2)))[1]);

                                    0.9091925189

@Markiyan Hirnyk  You're right of course. Think of it as a joke!

@Markiyan Hirnyk 

P:=a*b^2+sqrt(41)*b*c-a^3*c^2;

P1:=subs(sqrt(41)=d, a*b^2+sqrt(41)*b*c-a^3*c^2);

Q:=expand(P1^7);

ind:=indets(%) minus {d};

n:=igcd(seq(degree(Q,s), s=ind));

subs(d=sqrt(41), RealDomain[simplify](Q^(1/n), symbolic));

@Markiyan Hirnyk 

1) I'm not familiar enough with the theory of polynomial ideals and radicals in them. As I understand it from the original post, it is necessary for a given polynomial in several variables over real numbers just to find the root from it of maximum order, of course, if this root there exists.

2)  I did not compare my method with other methods of solving this problem.

3) I just answered that question OP   "Is there another commands for this?"

@MDD  This means that an assumption is imposed on the variable a. If you want the symbol tilda to be absent, click

Tools->Options->Display->Assumed variables->No Annotation-> Apply Globally

@MDD  You must (in the copiable form) provide the full text of the code in which this error occurs.