Revise integrator interface (again) (#185) #311

Job	Run time
Julia 1.10 - ubuntu-latest - x64 - push	11m 47s
Julia 1.10 - macOS-latest - x64 - push	11m 44s
Julia 1.10 - windows-latest - x64 - push	14m 32s
Julia ^1.11.0-0 - ubuntu-latest - x64 - push	16m 1s
Julia ^1.11.0-0 - macOS-latest - x64 - push	15m 59s
Julia ^1.11.0-0 - windows-latest - x64 - push	18m 5s
Julia nightly - ubuntu-latest - x64 - push	16m 22s
Julia nightly - macOS-latest - x64 - push	15m 22s
Julia nightly - windows-latest - x64 - push	17m 41s
	2h 17m 33s

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