Julia against Maple

Hi! More than a question, I am looking for a piece of advice for a project that I have.
Most of the optimization and equations that I have to resolve for my paper requires the usage of Maple. However, is there a way to do the same in Julia? If this is possible. How can I start? Which resources are required for that?
To give an example: most of the equation has this form:

You can compute 1d numerical integrals like this with e.g. the QuadGK.jl package.

If you need to solve this equation for x you can use e.g. Roots.jl (it’s pretty easy to take the derivative of that ratio with respect to x if you want to use Newton’s method).

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Great! thanks a lot for your answer! I will check the packages mentioned. One more thing, any book that you can recommend for that? Regards