Attack/Experience rewards

Quests
You can get Strength experience as rewards for completing certain quests:
 * 100 - The Blood Pact
 * 600 - In Search of the Myreque
 * 1,000 - Mountain Daughter
 * 2,000 - A Fairy Tale Part I
 * 2,000 - In Aid of the Myreque
 * 2,500 - Tai Bwo Wannai Trio
 * 2,812 - The Fremennik Trials
 * 3,000 - Death Plateau
 * 3,000 - Underground Pass
 * 3,075 - Heroes Quest
 * 4,000 - Quiet Before The Swarm
 * 4,825 - Vampire Slayer
 * 5,000 - TokTz-Ket-Dill
 * 7,500 - Spirit of Summer (if level 50 or higher)
 * 11,450 - Tree Gnome Village
 * 12,175 - Fight Arena
 * 13,750 - Waterfall Quest
 * 18,400 - The Grand Tree
 * 20,000 - Monkey Madness (optional when you speak to Daero, you can get 35,000 instead of 20,000 if you choose Attack and Strength over Defence and Constitution)

There are lots of quests and tasks that allows the player to choose the skill that will receive an experience reward. These are the choice rewards that can be spent on Attack, although it is reccomended to use them on skills that are harder to train. But it is recommended to put this experience into skills that are harder, slower, or more expensive to raise if the occasion allows.
 * A Fairy Tale Part II - A skill lamp granting 2,500 exp in any skill.
 * A Tail of Two Cats - Two antique lamps each granting 2,500 exp in any skill above level 30.
 * Blood Runs Deep - Three training sessions that grant 150,000 exp in any combat skill (except summoning) above level 75.
 * Contact! - Two 'wishes' each granting 7,000 exp in Attack, Summoning (if higher than level 30), Strength, Defence, Magic, Ranged, or Constitution.
 * Darkness of Hallowvale- A tome of experience with three chapters giving 2,000 experience each in any skill above level 30.
 * Dream Mentor - A Dreamy lamp which gives 15,000 exp in any combat skill except from Attack or Prayer.
 * The Fremennik Isles - Two lots of 10,000 exp that can be spent in Attack, Strength, Defence or Constitution.
 * Glorious Memories - A lamp received as an additional reward after the questgranting 2,500 exp in any skill and a tome with 3 chapters, each granting 5,000 exp in one of the following skills: Attack, Strength, Defence, Constitution, or Ranged.
 * The Great Brain Robbery - Blessed lamp granting 5,000 exp in any skill above 30.
 * King's Ransom - A skill lamp granting 5,000 exp in any skill above level 50.
 * Legacy of Seergaze - A tome of exp with three chapters, giving 2,500 exp each in any skill above 35.
 * Legends Quest - 7,650 experience in any four of the following skills: Attack, Defence, Strength, Constitution, Prayer, Magic, Woodcutting, Crafting, Smithing, Herblore, Agility, Thieving.
 * Love Story - After returning Mabel's ring to Mabel you receive a lamp granting 10,000 experience to any skill over level 60.
 * Meeting History - A skill book with 3 chapters, 2 chapters giving 1,000 exp and 1 with 500 exp in any skill above level 25.
 * Monkey Madness - 35,000 experience in Attack and Defence or Strength and Constitution, and 20,000 experience in the other two skills. Talk to Daero after the quest to receive these rewards. These 15,000 experience difference is not counted on the rewards per skill section above.
 * Myths of the White Lands - Provides 500 xp lamp in any skill.
 * One Small Favour - Two reward lamps granting 10,000 in any skill above level 30.
 * Recipe for Disaster - A lamp granting 20,000 in any skill above level 50.
 * Shadow of the Storm - 10,000 in any combat skill except prayer and summoning
 * The Tale of the Muspah - After completion, the player can talk to the natural historian for a lamp worth 200 xp in any skill.
 * Troll Stronghold - two skill lamps giving 10,000 in a skill above level 30.
 * Tutorial island or Learning the Ropes - Two xp lamps granting 250 experience in any nonmembers skill, other than Crafting, Runecrafting, or Dungeoneering.
 * While Guthix Sleeps - After talking with Idria you receive 4 lamps that grant 100,000 exp in any skill above level 65.


 * Observatory Quest - This quest grants 875 experience in Attack, Strength, Defence, or Constitution, depending on which constellation you observed during the quest, and this is completely random. (Some constellations do not give experience in any skill)
 * Swept away - This quest rewards includes 10 pieces of goulash, that each can give from 10 to 1,200 XP in the skill of the player's choice (The formula is: skill level * 10).
 * The Varrock Museum - After completing certain quests you can speak to Historian Minas and inform him of your discoveries and historical information. For this you will receive Kudos and at certain amounts of kudos you will receive lamps awarding small amounts of experience in any skill.
 * Nomad's Requiem - This quest rewards you with 70 Zeal Points, which can be spent, among other things, on experience in Strength (see below).

Tasks
Rewards for completing a diffculty section of a Task include experience lamps that can be used on any skill regardless of level.
 * 6 x 50,000 Experience Lamp
 * 1 x 40,000 Experience Lamp
 * 6 x 30,000 Experience Lamp
 * 1 x 28,000 Experience Lamp
 * 1 x 15,000 Experience Lamp
 * 4 x 10,000 Experience Lamp
 * 1 x 9,000 Experience Lamp
 * 1 x 7,500 Experience Lamp
 * 4 x 5,000 Experience Lamp
 * 1 x 1,500 Experience Lamp
 * 4 x 1,000 Experience Lamp
 * 1 x 500 Experience Lamp

Total experience = 645,500

Activities and Distractions and Diversions

 * Players can trade their Zeals, the rewards of the Soul Wars activity, for experience on attack among other things. The formula to calculate the attack experience gained per zeal is: (level^2/600) * 525, where "level" is the current attack level.
 * Players can trade their Void Knight commendation points, the rewards of the Pest Control activity, for experience on attack, among other things. The formula to calculate the attack experience gained per point is: 35 * ((level + 25) * (level -24) / 606), where "level" is the current attack level. You get a 1% bonus in the experience gained if you trade the points in a set of 10; similarly, you get 10% bonus if you trade the points in a set of 100.
 * Players can trade their Penguin points, the rewards of the Penguin Hide and Seek Distraction and Diversion, for experience in any skill or gold. You get 25 times your current level experience, in the skill of your choice.
 * Once a a player fully nourishes an Ancient Effigy, he/she will receive a Dragonkin lamp as a reward. The lamp will grant experience on the skill of your choice using the following formula where level is the current level of the chosen skill: ((level^3) - (2*level^2) + (100*level))/20.
 * Tears of Guthix (Distraction and Diversion), that is available after doing the quest of the same name, grants experience to the skill with the lowest amount of experience. The experience per tear collected caps at 60 exp, once the lowest skill reaches level 30.

Other

 * The miniquest Camelot training room grants 10,000 experience to Attack, Strength, Defence and Constitution, among other rewards, once it is completed.
 * You can use a Genie lamp that you can choose as a reward from any random event to receive experience equal to 10 times your current base level.
 * You can use a Book of knowledge that you can choose as a reward from the Surprise Exam! random event to receive experience equal to 15 times your current base level.