“Chi-Raq” is everything you’d expect from the polarizing filmmaker Spike Lee: smart, funny, wildly inventive, but also goofy, preachy and a little incoherent. The adjective “uneven” has described Lee’s work for some time now, but the best word for “Chi-Raq” might be “maddening.”

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The film’s title is a portmanteau of Chicago and Iraq, as an opening list of death tolls in both places makes clear. Chi-Raq is also the name of a rapper (a compelling Nick Cannon) trapped in a deadly gang war. These aren’t the Crips and the Bloods, though — they’re the Trojans and the Spartans. Chi-Raq’s main squeeze, played by Teyonah Parris (AMC’s “Mad Men”), is named Lysistrata.

Ring any bells, classics majors? “Chi-Raq” is based on Aristophanes’ play “Lysistrata,” about women who withhold sex until their men end the Peloponnesian war. In this version, when a little girl is killed by a stray bullet, Lysistrata spearheads a citywide sex strike: Nobody gets a piece before making peace. (That’s the movie’s pun, not mine.) The result is a battle of the sexes in which the men try everything — wooing, coaxing, playing slow jams — to loosen those chastity belts.

The moments of gonzo farce and incendiary satire work well, but “Chi-Raq” can’t avoid politically driven melodrama and lengthy soapboxing. John Cusack, playing a religious leader inspired by Chicago’s Father Michael Pfleger, is surprisingly convincing while railing against black-on-black crime, but a sermon is still a sermon. Samuel L. Jackson, as our cheerfully foulmouthed narrator, Dolmedes, is a far more entertaining figure.

“Chi-Raq” is packed with fine actors in small roles — Angela Bassett, Steve Harris, Jennifer Hudson — and includes welcome comebacks from Dave Chappelle and Wesley Snipes. Kudos to everyone for tackling the film’s rhyming dialogue, a mix of slam poetry and Shakespearean verse (written by Lee and Kevin Willmott) that ranges from clever to corny.

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The first production from Amazon Original Movies, “Chi-Raq” is tough to wholeheartedly recommend, but its topical themes and uncanny timing — arriving as anger over the police shooting of Laquan McDonald in Chicago is roiling anew — are worth noting. Whatever you think of Lee, he’s an artist engaged in the world and determined to make his own sense of it.