I would do the following:
download bmml source – Wireframes created with Balsamiq Mockups
Since they can only enter the expectation when they start the assignment, the "Start" button can persist the expectation to the database if it is provided before opening the modal or redirecting to the assignment page. If no text is entered, then the "start" button just opens the modal or redirects.
Even though there are two actions being taken, there is no need for two buttons because the end result (modal or redirect) is the same.
If the "start" button's action includes other data entry tasks, then you could probably include the expectation textbox along with the rest. However you would need to give us some more context about what happens after you click the button to be any more specific than that.
Regardless, given what you have included in your question, the above refinement is still an improvement.