  We present {bhpwave}: a new Python-based, open-source tool for generating the
gravitational waveforms of stellar-mass compact objects undergoing
quasi-circular inspirals into rotating massive black holes. These binaries,
known as extreme-mass-ratio inspirals (EMRIs), are exciting mHz gravitational
wave sources for future space-based detectors such as the Laser Interferometer
Space Antenna (LISA). Relativistic models of EMRI gravitational wave signals
are necessary to unlock the full scientific potential of mHz detectors, yet few
open-source EMRI waveform models exist. Thus we built {bhpwave}, which uses the
adiabatic approximation from black hole perturbation theory to rapidly
construct gravitational waveforms based on the leading-order inspiral dynamics
of the binary. In this work, we present the theoretical and numerical
foundations underpinning {bhpwave}. We also demonstrate how {bhpwave} can be
used to assess the impact of EMRI modeling errors on LISA gravitational wave
data analysis. In particular, we find that for retrograde orbits and
slowly-spinning black holes we can mismodel the gravitational wave phasing by
as much as $\sim 10$ radians without significantly biasing EMRI parameter
estimation.
