  4U 1957+11 is a black hole candidate system that has been in a soft X-ray
spectral state since its discovery. We present analyses of recent joint NICER
and NuSTAR spectra, which are extremely well-described by a highly inclined
disk accreting into a near maximally spinning black hole. Owing to the broad
X-ray coverage of NuSTAR the fitted spin and inclination are strongly
constrained for our hypothesized disk models. The faintest spectra are observed
out to 20 keV, even though their hard tail components are almost absent when
described with a simple corona. The hard tail increases with luminosity, but
shows clear two track behavior with one track having appreciably stronger
tails. The disk spectrum color-correction factor is anti-correlated with the
strength of the hard tail (e.g., as measured by the Compton $y$ parameter).
Although the spin and inclination parameters are strongly constrained for our
chosen model, the mass and distance are degenerate parameters. We use our
spectral fits, along with a theoretical prior on color-correction, an
observational prior on likely fractional Eddington luminosity, and an
observational prior on distance obtained from Gaia studies, to present mass and
distance contours for this system. The most likely parameters, given our
presumed disk model, suggest a 4.6 $\mathrm{M_\odot}$ black hole at 7.8 kpc
observed at luminosities ranging from $\approx 1.7\%$--$9\%$ of Eddington. This
would place 4U 1957+11 as one of the few actively accreting sources within the
`mass gap' of ${\approx} 2$--$5\,\mathrm{M_\odot}$ where there are few known
massive neutron stars or low mass black holes. Higher mass and distance,
however, remain viable.
