The solution is to use tuples when passing parameters to the files argument:
import requests
requests.post('http://example.com/example/asdfas', files={'value_1': (None, '12345'), 'value_2': (None, '67890')})
Works as expected:
'Accept': '*/*',
'Accept-Encoding': 'gzip, deflate, compress',
'Content-Length': '228',
'User-Agent': 'python-requests/2.2.1 CPython/3.3.2 Windows/7',
'Content-Type': 'multipart/form-data; boundary=85e90a4bbb05474ca1e23dbebdd68ed9'
--85e90a4bbb05474ca1e23dbebdd68ed9
Content-Disposition: form-data; name="value_1"
12345
--85e90a4bbb05474ca1e23dbebdd68ed9
Content-Disposition: form-data; name="value_2"
67890
--85e90a4bbb05474ca1e23dbebdd68ed9--