The dam took six years to complete, the lake 17 years to fill, the fish a few years to take up permanent residency and visitors about one trip to discover it.

Give or take a bus load or two, it is estimated that more than 3 million people will make a stop at the lake this year. And they are not just passing through anymore, they are staying awhile. Only one other national recreation site in the U.S. - Yosemite National Park - lures visitors into staying longer.Over the years, though, the lake has fooled a lot of people. Consider this: The lake was never expected to be a popular vacation spot. It was too far away and activities too limited to lure people. Nothing more than fish and water there. Boredom, they said, would set in quickly. That and the difficulty in getting there. By 1988, they predicted 25 years ago, visits might be up to, oh, 200,000 a year. That was if fishing improved.

Not only will 15 times the predicted number of people visit the shores this year, but many will have to cross U.S. borders to do so. Lake Powell, it appears, has established international appeal. On any given day, half the visiting tourists may not speak English well. They are coming to see the country.

A lake 186 miles long - with 1,960 miles of shoreline and 27 million acre-feet of water, enough to fill the water glasses of several trillion people - and a countryside accented by red and tan sandstone buttes, mesas, canyons and cliffs, has worldwide appeal. There is a beauty, visitors tell workers here, they've found nowhere else in their world travels.

Biggest attraction is, of course, Rainbow Bridge National Monument. It is the world's largest natural bridge - 290 feet high and spanning 275 feet. Though somewhat controversial, the rising lake has brought the bridge to millions . . . an easy two-hour boat ride from Wahweap, Halls Crossing or Bullfrog, then a short walk up a well-maintained trail. Some still prefer the old way of a long, hot hike in and a longer hike out over a rugged, unkept trail.

Fishing still remains one of the favorite pastimes for many. But even here, the lake fooled predictors.

Back when the lake was seen as an out-of-the-way spot that would get little consideration from most travelers, let alon fishermen, the trout was seen as the lake's main catch, and for the first few years it was. Then largemouth bass and crappie moved in, and the trout were pushed out. Rarely is a trout ever caught now.

While the lake was filling, Powell became a bass and crappie fish market. Good bass fishermen said their arms tired before the bass ever gave out. Not-so-good fishermen were taking crappie out of the lake by the bucketfuls. It would take far longer to clean the small fish than to catch them.

Then the stripers were introduced, and the largemouth and crappie faded.

Suddenly, fishing was better than a trip to the local fish vendor. It was harder to miss than to catch a striper. An anchovy on a No. 2 hook, dropped in a likely looking spot, was almost a guarantee. In one area near the Glen Canyon Dam, for example, an area about the size of four city blocks, stipers were coming out at an estimated rate of three tons per day . . . 150 fishermen, 10 fish limit, all in the three- to five-pound range, 1,500 fish, 6,000 pounds, roughly.

This was THE fish, experts predicted . . . easy to catch, plentiful, good eating, big. Trouble was, they were too plentiful and too big, in cases, and ate themselves almost out of existence. Two years ago there was a massive die-off. Millions starved.

So now attention is being turned to the smallmouth bass. It will be, they are now saying, as good as the largemouth was 10 years ago. Right now the court's out. Presently, largemouth and crappie fishing is getting better, as is striper fishing, and a few smallmouth are being caught.

But that's not all the lake offers. With little imagination a visitor can water ski, swim, boat, hike, camp, or just tour, anchoring a houseboat in a secluded cove or camping on a sandy beach, or just renting a room at the lodge.

The lake may have fooled the experts over the years, but the ones not fooled were the visitors. One look and they were hooked.