# problems with symbolic integration

I have recently asked a question on math.stackexchange concerning how to compute volumes of intersecting hypercubes and hyperspheres to which I got an extremely helpful answer. I would love to link there, but have insufficient karma.

Now, I'm trying to utilize `sage`

to generate some analytic solution for the lowest dimensionalities. With my very naive understanding of sage, the help of google and some trial & error, I came up with the following solution:

```
from sage.symbolic.integration.integral import integral
R = var("R")
assume(R>0)
x = var("x")
V0(R) = 1
V = [V0]
for i in range(1,3):
vlast = V[i-1]
vnew(R) = integral( vlast(R=sqrt(R**2 - x**2)),x,-min_symbolic(R,1),min_symbolic(R,1))
#,algorithm="fricas")
V.append(vnew)
print(V)
```

However, the output is not quite what I expected:

```
[R |--> 1, R |--> 2*min(1, R), R |--> 2*integrate(min(1, sqrt(R^2 - x^2)), x, -min(1, R), min(1, R))]
```

Somehow, the symbolic integrator seems unable to deal with this (relatively simple) function.
As you can see from the code, I've already tried using `fricas`

. That however results in

```
TypeError: sage1 := x=-min(R, 1)..min(R, 1)
There are 1 exposed and 2 unexposed library operations named min having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue
)display op min
to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation.
Cannot find a definition or applicable library operation named min with argument type(s)
Variable(R)
PositiveInteger
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.
```

I'm not sure what to make of this error message. Do I understand correctly that there is no implementation for `min`

available that is capable of dealing with a variable and an integer? That seems a little strange, given that this is such a fundamental functionality - or am I missing out on something here?

Any suggestion how to make it work are greatly appreciated!