"The Day the Earth Stood Cool" is the seventh episode of the twenty-fourth season of the American animated television series The Simpsons.
Fred Armisen, Carrie Brownstein, and Patton Oswalt guest star as the new family.
The Simpsons meet Terrance's wife Emily, his pet armadillo Chuy, their daughter Corduroy and their son T-Rex, and get their first exposure to their way of life.
While Homer and Lisa are immediately taken with the family, Bart is irritated by T-Rex's cynicism and Marge is uncomfortable in their presence, particularly of Emily's public breastfeeding.
Despite this, Marge supports Homer in his desire to fit in with their lifestyle, and allows him to combine their yard with the neighbor's into a "mono-yard" and lets him, Bart and Lisa accompany Terrance and T-Rex to rock shows, Mexican wrestling, roller derby, Korean gangster films and Modern Art exhibitions, even though she grows concerned that the kids are becoming pretentious.
The Simpsons are invited to T-Rex's birthday party, where Marge makes enemies of Emily and her fellow nursing mother friends by refusing to breast-feed Maggie.
Meanwhile, T-Rex mocks Homer's present and calls him a poseur, which angers Bart, and he starts a fight with him.
Homer and Terrance work together to put out the fire using large drums of baby formula Marge keeps in the garage.
Shortly after, the New York Times names Springfield 'America's Coolest City', which means it is played out.
Immediately upon hearing this, Terrance and Emily and the rest of the cool people move, much to Lisa's dismay.