Cheryl Miller was asked what her activities would include when she arrived in the nation's capital for this weekend's Maryland women's basketball invitational.

"I kind of wanted to see Lucky," said Miller, who took a liking to President Reagan's dog during a visit to the White House on a previous trip to Washington. "But he's been sent to the ranch."

Miller, Southern California's three-time all-America, will do many things while in the area, including play a lot of basketball.

She will be playing in this area for the first time when the Trojans meet St. Joseph's tonight at 7:30 at Cole Field House.

Maryland plays Bucknell at 9:30, and the winners play for the championship Saturday at 8 p.m.

Miller, a senior, said she had not seen a schedule of activities.

"But I'm sure they will keep me busy," she said. "I'm excited. The best thing about it is seeing my oldest brother, who is in the Air Force (stationed at Andrews Air Force Base)."

Miller, one of the most prolific women's college basketball players ever, is playing for a team that beat its first two opponents, Brigham Young and Pepperdine, 102-53 and 94-50.

"We're playing very well," said Miller of the Trojans, a young team last year that finished 21-9 and lost in the second round of the NCAA tournament. "We're controlling the boards better. And I think we're a quicker team than last year. We're running well. In the preseason conditioning drills, I saw a lot of desire."

Says Maryland Coach Chris Weller of Miller, who is averaging 29 points and 12.5 rebounds: "She's like two people on the court."

Miller says her life the last few years -- including two most valuable player awards, two national championship seasons and a gold medal in the 1984 Olympics -- has been "exciting, busy and frustrating. But I like the attention."

But she is not going to allow her senior year to be a letdown. "I'm a spiritual leader on the court," she says. "I'd like to finish on a winning note."

In the first round, the Trojans will play St. Joseph's, which was 25-5 last year and has been ranked as high as 20th in the preseason polls. Maryland, which won its first two games -- against Monmouth (65-63) and American (64-60) -- plays Bucknell (1-1), led by sophomore center Marie Kocornik (22 points).

The Terrapins are in a lot better shape than they could have been. Freshman Deana Tate, the starting point guard who was involved in Weller's recent reprimand for a recruiting violation, was cleared by the NCAA Subcommittee on Appeals to play this season. In her first game, against American, she scored 17 points.

Chequita Wood, who has been injured and who missed a great deal of preseason practice, had 22 points against the Eagles. She won't be at full strength for another month but leads the Terrapins in scoring with a 19-point average.

"I think we will have to really concentrate on Bucknell," said Weller. "If we get by, then we will have to play a respectable championship game. I just want us to have a tournament where we learn more. I'm not saying we can't win it, but it will take an extraordinary effort.

"We have made some preparations (in case we play USC), but we mostly have to concentrate on our team rather than another team or player."