$\tanh^{-1}$ of any real number whose modulus is $1$ or greater than $1$ is meaningless. So the following double integral must be meaningless. But when I computed the following double integral in Wolfram alpha, it did not show any integrand error:
Obviously $\sqrt{300-20y+y^2-20z+z^2}$ is greater than $y-10$ for any real $y$ and $z$. So what is wrong here?
EDIT: Have a look at here. Wolfram is neither showing error or complex values. What does it mean?
This may explain what Wolfram Alpha is doing:
https://www.wolframalpha.com/input?i=tanh%5E-1%282%29
This shows that Wolfram Alpha will treat $\tanh^{-1}$ as a complex-valued function when you give it input that is outside the domain of the real-valued $\tanh^{-1}$ function.
In your example, Wolfram Alpha appears to be integrating $\tanh^{-1}$ as a function with complex values since you gave it an integral that cannot be integrated assuming $\tanh^{-1}$ is a real-valued function.
Note that in this case it gave you a complex result at the end, not a real number: it includes the term $4.54747\times 10^{-13}i.$ Due to the very small size of this term, I suspect that it is actually due to numerical error in the calculation and that a more exact calculation would have completely canceled out any imaginary components. In the second example the cancellation may work out exactly, as numerical calculations sometimes do. As suggested in a comment, you may be able to see a meaningful imaginary component (not just numerical error) if you try different bounds of integration.