The Open Writing Assignment
So it's basically a semi-open writing assignment, but you must choose where to specify that also fits within the umbrella of the question. Like "Analyze the role of a character in Dante's The Inferno" just added an extra degree of freedom with the character being analyzed whereas "Analyze the role of Virgil in Dante's The Inferno" is now a semi-open writing assignment. The open writing assignment gives the advantage of allowing you to write about something you know well.