`RHO LOSS` integration test

[XianzheMa]

Per the title.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 82.56%. Comparing base (5bd3230) to head (c9f2eb1).

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #509 +/- ## ========================================== + Coverage 82.48% 82.56% +0.07% ========================================== Files 214 214 Lines 9962 9966 +4 ========================================== + Hits 8217 8228 +11 + Misses 1745 1738 -7 ```

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[github-actions[bot]]

^{( % to main) ( % to main)}