  There are so many ideas that potentially explain the dark energy phenomenon,
current research is focusing on a more in-depth analysis of the potential
effects of modified gravity on both local and cosmic scales. In this paper we
have investigated some cosmic reconstructions in $f (Q)$ cosmology where $Q$ is
the non-metricity corresponding to the evolution background in the
Friedmann-Lamatre-Robertson-Walker $(FLRW)$ universe. This allows us to
determine how any $FLRW$ cosmology can emerge from a particular $f (Q)$ theory.
We employ the reconstruction technique to generate explicit formulations of the
$f (Q)$ Lagrangian for several types of matter sources like perfect fluid, dust
like fluid, stiff fluid and the binary mixture of two fluids. Furthermore, we
computed the field equations and equation of state (EoS) parameter $\omega$ for
two different reconstructed $f(Q)$ models with the variation of the involved
constants, which gives the scenario of accelerating universe, quintessence
region and cosmological constant. We also observed that the time dependence of
$\omega$ admits cosmic acceleration. These new $f(Q)$ gravity inspired models
may have an impact on gravitational phenomena at other cosmological scales.
