  We present constraints on the mean matter density, Omega_m, the normalization
of the density fluctuation power spectrum, sigma_8, and the dark-energy
equation-of-state parameter, w, obtained from measurements of the X-ray
luminosity function of the largest known galaxy clusters at redshifts z<0.7, as
compiled in the Massive Cluster Survey (MACS) and the local BCS and REFLEX
galaxy cluster samples. Our analysis employs an observed mass-luminosity
relation, calibrated by hydrodynamical simulations, including corrections for
non-thermal pressure support and accounting for the presence of intrinsic
scatter. Conservative allowances for all known systematic uncertainties are
included, as are standard priors on the Hubble constant and mean baryon
density. We find Omega_m=0.28 +0.11 -0.07 and sigma_8=0.78 +0.11 -0.13 for a
spatially flat, cosmological-constant model, and Omega_m=0.24 +0.15 -0.07,
sigma_8=0.85 +0.13 -0.20 and w=-1.4 +0.4 -0.7 for a flat, constant-w model.
Future work improving our understanding of redshift evolution and observational
biases affecting the mass--X-ray luminosity relation have the potential to
significantly tighten these constraints. Our results are consistent with those
from recent analyses of type Ia supernovae, cosmic microwave background
anisotropies, the X-ray gas mass fraction of relaxed galaxy clusters, baryon
acoustic oscillations and cosmic shear. Combining the new X-ray luminosity
function data with current supernova, cosmic microwave background and cluster
gas fraction data yields the improved constraints Omega_m=0.269 +- 0.016,
sigma_8=0.82 +- 0.03 and w=-1.02 +- 0.06. (Abridged)
