[Python] Building a connection between a LLM on hugging face and a Web app frontend

I'm kind of new to the scene. I want to develop a math app for a science competition and I'm kind of still in the planning phase of things.

I want to know if its possible to fine tune a model on hugging face and then use hugging face as a location from which my Web app can access the LLM/Transformer. If this can be done, how exactly would one go about connecting the front end and back end?

I'm assuming I'd use hugging face APIs but is there anything else I need to keep on mind? Anything else I need to take into consideration?

Also, would the frontend have to be built in something like gradio?

If I can't use hugging face for this, could anyone please suggest an alternative I could use for this purpose (storing the LLM on the cloud/ not on my machine) and how would I go about building my app?possibly using flask?

It would be great if it were free or very low cost

Thank you so much

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