  Motivated by a new model of nonlinear electrodynamics known as Modified
Maxwell (ModMax) theory, an exact analytical solution for black holes is
obtained by coupling ModMax nonlinear electrodynamics and $F(R)$ gravity. Then,
the effects of the system's parameters ($F(R)$-ModMax gravity parameters) on
the event horizons are analyzed. The obtained black holes thermodynamic
properties in the $F(R)$-ModMax theory are investigated by extracting their
thermodynamic quantities such as Hawking temperature, electric charge, electric
potential, entropy, and also total mass. The first law of thermodynamics for
the system under study is evaluated. Next, by considering these black holes,
the impact of various parameters on both the local stability and global
stability are investigated by examining the heat capacity and the Helmholtz
free energy, respectively. Finally, the thermodynamic geometry of the black
hole in $F(R)$-ModMax gravity is investigated by applying the thermodynamic
metric (the HPEM metric).
