  We present a new determination of the evolving galaxy UV luminosity function
(LF) over the redshift range $9.5<z<12.5$ based on a wide-area ($>250$
arcmin$^2$) data set of JWST NIRCam near-infrared imaging assembled from
thirteen public JWST surveys. Our relatively large-area search allows us to
uncover a sample of 61 robust $z>9.5$ candidates detected at $\geq 8\sigma$,
and hence place new constraints on the intermediate-to-bright end of the UV LF.
When combined with our previous JWST+UltraVISTA results, this allows us to
measure the form of the LF over a luminosity range corresponding to four
magnitudes ($M_{1500}$). At these early times we find that the galaxy UV LF is
best described by a double power-law function, consistent with results obtained
from recent ground-based and early JWST studies at similar redshifts. Our
measurements provide further evidence for a relative lack of evolution at the
bright-end of the UV LF at $z=9-11$, but do favour a steep faint-end slope
($\alpha\leq-2$). The luminosity-weighted integral of our evolving UV LF
provides further evidence for a gradual, smooth (exponential) decline in
co-moving star-formation rate density ($\rho_{\mathrm{SFR}}$) at least out to
$z\simeq12$, with our determination of $\rho_{\mathrm{SFR}}(z=11)$ lying
significantly above the predictions of many theoretical models of galaxy
evolution.
