  Our goal is to calculate the circular velocity curve of the Milky Way, along
with corresponding uncertainties that quantify various sources of systematic
uncertainty in a self-consistent manner. The observed rotational velocities are
described as circular velocities minus the asymmetric drift. The latter is
described by the radial axisymmetric Jeans equation. We thus reconstruct the
circular velocity curve between Galactocentric distances from 5 kpc to 14 kpc
using a Bayesian inference approach. The estimated error bars quantify
uncertainties in the Sun's Galactocentric distance and the spatial-kinematic
morphology of the tracer stars. As tracers, we used a sample of roughly 0.6
million stars on the red giant branch stars with six-dimensional phase-space
coordinates from Gaia data release 3 (DR3). More than 99% of the sample is
confined to a quarter of the stellar disc with mean radial, rotational, and
vertical velocity dispersions of $(35\pm 18)\,\rm km/s$, $(25\pm 13)\,\rm
km/s$, and $(19\pm 9)\,\rm km/s$, respectively. We find a circular velocity
curve with a slope of $0.4\pm 0.6\,\rm km/s/kpc$, which is consistent with a
flat curve within the uncertainties. We further estimate a circular velocity at
the Sun's position of $v_c(R_0)=233\pm7\, \rm km/s$ and that a region in the
Sun's vicinity, characterised by a physical length scale of $\sim 1\,\rm kpc$,
moves with a bulk motion of $V_{LSR} =7\pm 7\,\rm km/s$. Finally, we estimate
that the dark matter (DM) mass within 14 kpc is $\log_{10}M_{\rm DM}(R<14\,
{\rm kpc})/{\rm M_{\odot}}= \left(11.2^{+2.0}_{-2.3}\right)$ and the local
spherically averaged DM density is $\rho_{\rm
DM}(R_0)=\left(0.41^{+0.10}_{-0.09}\right)\,{\rm
GeV/cm^3}=\left(0.011^{+0.003}_{-0.002}\right)\,{\rm M_\odot/pc^3}$. In
addition, the effect of biased distance estimates on our results is assessed.
