mitr argument is a argument of the function scipy.optimize.cython_optimize.brentq that is set to 10 on the reference guide https://docs.scipy.org/doc/scipy/reference/optimize.cython_optimize.html.
How the brentq function uses this argument? Could not find any explanation about it.
Yes, mitr in scipy.optimize.cython_optimize documentation examples corresponds to maxiter in brentq, bisect, ridder, etc. I agree it's confusing, and maxiter would've been a better choice for consistency, but it's only an example, perhaps it can still be updated. The underlying C & Cython functions use iter which is a keyword in Python. You will find the Cython headers in cython_optimize/_zeros.pxd and the zero function signatures in the zeros header scipy/optimize/zeros.h. The order of arguments are almost the same. Sorry