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Apple certainly doesn't let you.

There are several apps[0] off the top of my head that pull data from Apple's HealthKit. Apple even has a framework for it: HealthKit. That said, I've never written to that API myself, but it observational evidence indicates that you can pull data from Apple just fine. The app I use to pull data off Apple and ship to Strava says as much.

[0] RunGap and HealthFit

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you can use https://github.com/cyberjunky/python-garminconnect to pull your data from garmin, I've been using it daily with no issues
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Polar has an API where you can get more or less anything out. That bit is fine - sadly you can't put things in (like virtual cycling, or any activities not recorded on the Polar).
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