How to do this REST API call in Python?

Something like this should do the job :

auth = HTTPBasicAuth('aa43ae0a-a7a7-4016-ae96-e253bb126aa8', '1662[....]549') payload = { "startDate": "2016-05-15" , "endDate": "2016-05-16", "format": "tsv", "dataset": "appStart", } url = "https://analytics.cloud.unity3d.com/api/v2/projects/aa43ae0a-a7a7-4016-ae96-e253bb126aa8/rawdataexports" result = requests.post(url, json=payload, auth=auth) 

1. Authentication : --user argument of curl comand allows to setup an HTTP Basic Auth
2. --data was a JSON payload, while the requested content-type is configured (via headers) with Content-Type: application/json. Simplify this with requests using json argument and passing a valid python dict as payload. The payload will be converted to json, and the correct header will be added to the request to retrieve a response with json data.

Be careful ! In your question, you provided the user/password used to call this REST API. If this information is the real one, posting it on Stack Overflow is probably a security issue !