  Within the context of metric-affine gravity, we examine the significance of
the boundary term in symmetric teleparallel gravity by employing the
cosmological dynamical system analysis method. We focus on the novel gravity
models characterized by the functions $f(Q,C)$, where $f$ is a smooth function
of the non-metricity scalar $Q$ and the associated boundary term $C$. In a
cosmological setting adopting three different classes of symmetric teleparallel
affine connections, we investigate a model $f(Q,C)=Q^{s}+eC^{r}$, and some
special cases of this model. We show that the boundary term which is added to
the Einsteinian field equations (or equivalently to $f(Q)=Q$ ones) are capable
of bringing forward solutions corresponding to the early accelerated expansion.
This alludes the physics behind the boundary terms which usually are discarded
in the most gravitational theories.
