New to Julia -- EAGO Nonlinear model works when finding Min but not Max?

This looks like a bug in EAGO.

You might like to try Juniper and the latest version of JuMP: GitHub - lanl-ansi/Juniper.jl: A JuMP-based Nonlinear Integer Program Solver

But if you dont have integer variables, you should first try Ipopt: GitHub - jump-dev/Ipopt.jl: Julia interface to the Ipopt nonlinear solver

The jump documentation has a bunch of nonlinear tutorials to get you started: Introduction · JuMP