The number $10.3500574150076$ is a numeric approximation of $\log(2)^2+\pi^2$. It has a relatively simple form. But I have tried Maple's identify, ISC+, wolframalpha, and none of these could find a closed form of it. Is there anyway to find its closed form with algorithm/software?
My impression is that these software do a good job in detecting integer relationship between well-known constants, i.e., the form of like $3 \cdot \log(2)+1/2 \cdot \pi$. But they have trouble with detecting linear combinations of products like $\log(2)^2+\pi^2$ or $\pi\log(2)+\pi^2$.
It can be easily done, in this case, with RIES by Robert Munafo written in C. As with any software, it has it limitations but it can be useful.