Cut-off frequency of partially filled waveguide

Hi everyone,

I am new to waveguide analysis and I need to calculate the cut-off frequency of partially filled waveguide using the equations (8-118) for TE0n and (8-130) for TM1n of Advanced engineering electromagnetic by Balanis by Matlab.
Attached images are the mentioned equations.
I would be grateful if any one can help me to write a Matlab code for this equations or can send me a code that they have for this problem.

I am looking forward to hearing from you as soon as possible.

best regards,