Testing notebooks: Inject query parameters into embedded app?

[liquidcarbon]

Suppose I have a notebook that accepts query params ([live here])(https://liquidcarbon-puppy-hf-marimo.hf.space/?file=notebooks%2Fmultiplier.py)

import marimo

__generated_with = "0.14.13"
app = marimo.App(width="medium")


@app.cell
def _():
    import marimo as mo

    qp = mo.query_params()
    ui = mo.md(
        '''
        - What's x?: {x}
        - How many times?: {y}
        '''
    ).batch(
        x=mo.ui.slider(start=1, stop=10, value=3, include_input=True),
        y=mo.ui.slider(start=1, stop=10, value=3, include_input=True)
    )
    return qp, ui


@app.cell
def add(qp, ui):
    z = ui["x"].value * ui["y"].value
    qp, ui, z
    return


if __name__ == "__main__":
    app.run()

And I made up a test for it using app.embed (it passes):

import asyncio
from multiplier import app

result = asyncio.run(app.embed())
defs = result.defs._dict
print(defs.get("qp"))

def test_z_is_defined():
  z = defs.get("z")
  assert z
  print(z)

Is there a way to inject query params into app?
I was poking around the objects under app._execution_context._kernel and it seems like it should be possible to construct mock execution context with desired query params? But so far I failed to modify the result.

Why?

Being able to do this would unlock automated testing of notebooks with different user inputs (if they're coupled to query params).