Two examples:

for i in {1, 2/0, -3, 1/4, 5} do

if i::posint then print(i)  fi;

od;

       Error, numeric exception: division by zero

select(x->is(x::posint), {1, 2/0, -3, 1/4, 5});

       Error, numeric exception: division by zero

How to avoid interruption of the program in such cases?

My attempt:

RealDomain[solve]({x^2+y^2+z^2 = 3, x+y+z = 3}, {x,y,z});

             {x = -RootOf(_Z^2+(z-3)*_Z+z^2-3*z+3)-z+3, y = RootOf(_Z^2+(z-3)*_Z+z^2-3*z+3), z = z}

In fact, the system in the real domain has a unique solution x = 1, y = 1, z = 1. It is easy to find by hand, noting that the plane  x + y + z = 3  is tangent to the sphere  

The second graph is incorrect. The reason?

plots[polarplot]([3+cos(4*t), 2-cos(4*t)], t = 0 .. 2*Pi)

Here is , seemingly simple task:
In the Euclidean plane are given two sets, each with 4 points. It is known that all possible pairwise distances between the points of the first set coincide with all possible pairwise distances between the points of the second set, ie we obtain two sets of numbers, in each of which six numbers. Of course, the numbers in each numeric set can be repeated (such sets are called multisets).  Can we say that there is an isometry of...

Maple 13 does not calculate the definite integral

int(x^4/(4*x^5+2), x=0..1);

although the corresponding indefinite integral is calculated correctly. The reason?

Thank you.