The beast-king is the king in Daniel 11:36
Daniel 11:
36 And the king shall do according to his will; and he shall exalt himself, and magnify himself above every god, and shall speak marvellous things against the God of gods, and shall prosper till the indignation be accomplished: for that that is determined shall be done.
Revelation 13:
4 And they worshipped the dragon which gave power unto the beast: and they worshipped the beast, saying, Who is like unto the beast? who is able to make war with him?
5 And there was given unto him a mouth speaking great things and blasphemies; and power was given unto him to continue forty and two months.
6 And he opened his mouth in blasphemy against God, to blaspheme his name, and his tabernacle, and them that dwell in heaven.
Revelation 17:
10 And there are seven kings: five are fallen, and one is, and the other is not yet come; and when he cometh, he must continue a short space.
11 And the beast that was, and is not, even he is the eighth, and is of the seven, and goeth into perdition.
The little horn > becomes the prince who shall come > becomes the Antichrist > becomes the revealed man of sin > becomes the beast-king.
In Daniel 11:45, the beast-king will meet his end there on the temple mount when Jesus returns and casts him into the lake of fire.
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Daniel 11:36 is about the king of the north as much of the entire chapter is.
Daniel 11:
36 And the king shall do according to his will; and he shall exalt himself, and magnify himself above every god, and shall speak marvellous things against the God of gods, and shall prosper till the indignation be accomplished: for that that is determined shall be done.
Now let's try to keep the one verse you take out of context in context ,shall we.
Daniel 11
21 And in his estate shall stand up a vile person, to whom they shall not give the honour of the kingdom: but he shall come in peaceably, and obtain the kingdom by flatteries.
22 And with the arms of a flood shall they be overflown from before him, and shall be broken; yea, also the prince of the covenant.
23 And after the league made with him he shall work deceitfully: for he shall come up, and shall become strong with a small people.
24 He shall enter peaceably even upon the fattest places of the province; and he shall do that which his fathers have not done, nor his fathers' fathers; he shall scatter among them the prey, and spoil, and riches: yea, and he shall forecast his devices against the strong holds, even for a time.
25 And he shall stir up his power and his courage against the king of the south with a great army; and the king of the south shall be stirred up to battle with a very great and mighty army; but he shall not stand: for they shall forecast devices against him.
26 Yea, they that feed of the portion of his meat shall destroy him, and his army shall overflow: and many shall fall down slain.
27 And both of these kings' hearts shall be to do mischief, and they shall speak lies at one table; but it shall not prosper: for yet the end shall be at the time appointed.
28 Then shall he return into his land with great riches; and his heart shall be against the holy covenant; and he shall do exploits, and return to his own land.
29 At the time appointed he shall return, and come toward the south; but it shall not be as the former, or as the latter.
30 For the ships of Chittim shall come against him: therefore he shall be grieved, and return, and have indignation against the holy covenant: so shall he do; he shall even return, and have intelligence with them that forsake the holy covenant.
31 And arms shall stand on his part, and they shall pollute the sanctuary of strength, and shall take away the daily sacrifice, and they shall place the abomination that maketh desolate.
32 And such as do wickedly against the covenant shall he corrupt by flatteries: but the people that do know their God shall be strong, and do exploits.
33 And they that understand among the people shall instruct many: yet they shall fall by the sword, and by flame, by captivity, and by spoil, many days.
34 Now when they shall fall, they shall be holpen with a little help: but many shall cleave to them with flatteries.
35 And some of them of understanding shall fall, to try them, and to purge, and to make them white, even to the time of the end: because it is yet for a time appointed.
36 And the king shall do according to his will; and he shall exalt himself, and magnify himself above every god, and shall speak marvellous things against the God of gods, and shall prosper till the indignation be accomplished: for that that is determined shall be done.
37 Neither shall he regard the God of his fathers, nor the desire of women, nor regard any god: for he shall magnify himself above all.
38 But in his estate shall he honour the God of forces: and a god whom his fathers knew not shall he honour with gold, and silver, and with precious stones, and pleasant things.
39 Thus shall he do in the most strong holds with a strange god, whom he shall acknowledge and increase with glory: and he shall cause them to rule over many, and shall divide the land for gain.
40 And at the time of the end shall the king of the south push at him: and the king of the north shall come against him like a whirlwind, with chariots, and with horsemen, and with many ships; and he shall enter into the countries, and shall overflow and pass over.
41 He shall enter also into the glorious land, and many countries shall be overthrown: but these shall escape out of his hand, even Edom, and Moab, and the chief of the children of Ammon.
42 He shall stretch forth his hand also upon the countries: and the land of Egypt shall not escape.
43 But he shall have power over the treasures of gold and of silver, and over all the precious things of Egypt: and the Libyans and the Ethiopians shall be at his steps.
44 But tidings out of the east and out of the north shall trouble him: therefore he shall go forth with great fury to destroy, and utterly to make away many.
45 And he shall plant the tabernacles of his palace between the seas in the glorious holy mountain; yet he shall come to his end, and none shall help him.
Not that you can understand any of this.You didn't even know the king of the north had a fleet of ships.