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We present {bhpwave}: a new Python-based, open-source tool for generating thegravitational waveforms of stellar-mass compact objects undergoingquasi-circular inspirals into rotating massive black holes. These binaries,known as extreme-mass-ratio inspirals (EMRIs), are exciting mHz gravitationalwave sources for future space-based detectors such as LISA. Relativistic modelsof EMRI gravitational wave signals are necessary to unlock the full scientificpotential of mHz detectors, yet few open-source EMRI waveform models exist.Thus we built {bhpwave}, which uses the adiabatic approximation from black holeperturbation theory to rapidly construct gravitational waveforms based on theleading-order inspiral dynamics of the binary. In this work, we present thetheoretical and numerical foundations underpinning {bhpwave}. We alsodemonstrate how {bhpwave} can be used to assess the impact of EMRI modelingerrors on LISA gravitational wave data analysis. In particular, we find thatfor retrograde orbits and slowly-spinning black holes we can mismodel thegravitational wave phasing by as much as $\sim 10$ radians withoutsignificantly biasing EMRI parameter estimation.

BHPWAVE: An adiabatic gravitational waveform model for compact objects undergoing quasi-circular inspirals into rotating massive black holes