  In this work, a spherically symmetric and static relativistic anisotropic
fluid sphere solution of the Einstein field equations is provided. To build
this particular model, we have imposed metric potential $e^{2\lambda(r)}$ and
an equation of state. Specifically, the so-called modified generalized
Chaplygin equation of state with $\omega=1$ and depending on two parameters,
namely, $A$ and $B$. These ingredients close the problem, at least
mathematically. However, to check the feasibility of the model, a complete
physical analysis has been performed. Thus, we analyze the obtained geometry
and the main physical observables, such as the density $\rho$, the radial
$p_{r}$, and tangential $p_{t}$ pressures as well as the anisotropy factor
$\Delta$. Besides, the stability of the system has been checked by means of the
velocities of the pressure waves and the relativistic adiabatic index. It is
found that the configuration is stable in considering the adiabatic index
criteria and is under hydrostatic balance. Finally, to mimic a realistic
compact object, we have imposed the radius to be $R=9.5\ [km]$. With this
information and taking different values of the parameter $A$ the total mass of
the object has been determined. The resulting numerical values for the
principal variables of the model established that the structure could represent
a quark (strange) star mixed with dark energy.
