[Feature]: Integration tests

### 💡 Feature Description and Proposed Solution

We should add more integration tests especially for the instrumentations and make them run in the CI.

### 🤔 Related Problem

_No response_

### 🤝 Contribution

- [ ] Yes, I'd be happy to submit a pull request with these changes.
- [ ] I need some guidance on how to contribute.
- [ ] I'd prefer the AgentOps team to handle this update.

### Development

This issue is being worked on in branch: `cursor/create-integration-tests-for-examples-2165`