July 22, 20XX
While learning about this colonized planet's history, there were some points that stood out to me. In the age of advanced space technology, the colonization of distant planets became a common venture for humanity. Among the many planets they settled, one stood out due to its diverse and intelligent life forms. This planet, housed three prominent civilizations: the royal toadstools, the aristocratic animal humanoids, and the rapidly growing society of Hyrule.
Mega City, a prominent hub of scientific development, was a thriving metropolis that welcomed beings from across the galaxy. It served as a melting pot of cultures, knowledge, and technology. It was here that two of the most famous icons of the galaxy would soon rise to prominence, setting the stage for a legendary conflict that would shape the destiny of this plane and beyond.
In Mega City, brilliant scientists was on the verge of a groundbreaking discovery. They had been working tirelessly on a project called the "Interstellar Transcendence Engine" (ITE), a technology capable of traversing vast distances in the blink of an eye. With the ITE, intergalactic travel would no longer be a mere dream, and the possibilities for trade, diplomacy, and exploration would become limitless.
On the other side of the planet, a mysterious and enigmatic figure known as the "Wanderer of the Stars" had arrived in Hyrule. This wanderer was a being of immense power and wisdom, known to have wandered the cosmos for eons, witnessing the rise and fall of countless civilizations. The Wanderer, now in a humanoid form, carried with them ancient artifacts and knowledge that had the potential to reshape reality itself.
As news of the ITE's development and the presence of the Wanderer spread throughout the galaxy, intrigue and tensions escalated. Factions from different planets sought to control these two icons for their own purposes. Some saw the ITE as a means to expand their influence, while others believed the Wanderer's wisdom could grant them god-like powers.
In Mega City, many researchers and scientists faced constant pressure from governments, corporations, and secretive organizations that sought to gain control of the ITE. Aware of the dangers his invention posed if misused, he hesitated to release it to the public. Meanwhile, in Hyrule, the Wanderer had become a revered figure, and some sought to serve and protect them, while others saw them as a threat and sought to eliminate the potential danger.
In the midst of the brewing conflict, a chance encounter between the scientists and the Wanderer occurred in Mega City. They found a mutual respect for each other's goals and beliefs. They realized that the best way to prevent this planet from descending into chaos was to guide its inhabitants toward cooperation, rather than confrontation.
United by their shared vision of a harmonious galaxy, they worked together to host a historic summit in Mega City. Leaders from this planet and beyond were invited, including representatives from the royal toadstools, animal humanoids, and Hyrule. The summit aimed to foster understanding, trust, and cooperation among the civilizations, with the ITE and the Wanderer's knowledge as potential tools for peaceful exploration and advancement.
However, not everyone at the summit was convinced of the need for cooperation. Some factions saw the ITE and the Wanderer as threats that could upset the balance of power they had established. As tensions reached a boiling point, the fate of this planet and the galaxy hung in the balance.
The epic showdown between conflicting ideologies and powerful forces would determine the course of history. Backed by allies from all three civilizations, stood together to face the challenges that lay ahead. It was a test of humanity's potential for enlightenment and compassion, as well as the ability of this planet's diverse inhabitants to unite as one.
In the end, the true power of the ITE and the Wanderer's knowledge was not in dominance but in fostering harmony and mutual understanding among civilizations. The summit succeeded in persuading the factions to put aside their differences and embrace a new era of cooperation and peaceful coexistence.
Beacons of unity and progress, became revered figures across the galaxy. Their legacy transcended time and space, inspiring future generations to seek knowledge, understanding, and cooperation, and to use technology for the betterment of all.
And so, the age of advanced space technology continued, but it was now marked by an era of enlightenment, where the galaxy embraced the values of this planet and its iconic heroes, forever changing the course of the stars.
Key scientific figures, Dr. Elvin Gadd and Dr. Julian "Ovi" Kintobor, continued their experiments and research in the continents of the Mushroom Kingdom and Mobius, their discoveries and collaborations with Dr. Ellidy and Sir Charles the Hedgehog only grew more exciting and insightful. They learned about the thriving communities living beyond the Mushroom Kingdom's borders, from the families of intelligent monkeys in the dense jungle, to the tribes of Goombas coexisting in harmony with the local flora and fauna, and the wondrous place known as Dream Land, where innovation and imagination came to life.
As the Mushroom Kingdom faced challenges from refugees fleeing the aftermath of the Great War and the rise of crime orchestrated by the notorious "ShyGuys" gang, Dr. Kintobor realized that unity and cooperation among the various species in the land were crucial. He sought to create a sanctuary where all Mobians, as they began to refer to themselves, could live in harmony under the fair and just rule of the Acorn Royal Family.
With the support of Dr. Ellidy, Sir Charles, and many other like-minded individuals, Dr. Kintobor established the Mobian Sanctuary. It was a place of refuge and learning, where different species and anthropomorphic beings from all corners of the Mushroom Kingdom and beyond could come together to share knowledge, culture, and ideas. The sanctuary acted as a hub for scientific research, technological advancement, and cultural exchange, fostering peace and understanding among the various communities.
As the Mobians thrived under the Acorn Royal Family's benevolent leadership, their curiosity and thirst for exploration led some adventurous individuals to reach for the stars. Inspired by the legends of cosmic entities and ancient myths, they built advanced spacecraft and embarked on daring space expeditions, exploring distant planets and discovering other civilizations such as Corneria and the Bem High Council.
With each successful space mission, the Mobians' horizons expanded, and they encountered beings from distant galaxies, exchanging knowledge and forming alliances. They learned about advanced technologies, mystical powers, and new forms of energy that could potentially benefit their own world. The Mobian Sanctuary became a beacon of intergalactic cooperation, attracting visitors from across the cosmos.
As the years passed, the Mushroom Kingdom saw a significant reduction in crime and conflict, thanks to the Mobian Sanctuary's influence and the thriving cultural exchanges among its residents.
He befriended a young brown hedgehog (the nephew of Sir Charles; young sentient hedgehogs are first brown until they tend to get older whereas their fur changes into different colors and they develop unique abilities) and a young adult human plumber who currently reside in the Mushroom Kingdom area with his younger abit-taller brother in the technical business.
Suddenly a freak accident occurred by Ovi's experiment, where he wanted to solve the brutal conflicts on this planet with unique resources from the planet (nicknamed Power-Ups), between a Super-Star and Chaos Emeralds used within Retro-Orbital Chaos Computer (ROCC) which was splattered by a rotten egg. This shockwave blasted Kintobor into an evil personality, making the turtle absorb powers that made him a monstrous Koopa, upgrading and accelerating young Sonic's gift of speed-making his fur blue, and giving the Mario brothers (who were young adults at that time, enough to witness it) meta-human abilities.
Math Notes: (filled with academic musings)
Integral pi/2,0 (7 sin x - 2 cos x) dx
(-7 cos x - 2 sin x) | pi/2,0
(-7 cos (pi/2) - 2 sin (pi/2)) - (-7 cos (0) - sin (0))
= -2 - (-7)
= 5
If a polynomial; use the power rule: #(n^x+1 / x+1)
Integral 1,0 3(4x+x^4)(10x^2 + x^5 -2)^6 dx
u=10x^2 + x^5 - 2
du/dx = 20x + 5x^4
du/dx = 5(4x + x^4)
dx = du / 5(4x+x^4)
Integral 1,0 3(4x+x^4) u (du / 5(4x+x^4))
3/5 Integral udu = 3/5 (u^2 / 2) |1,0
= 3/10 (10x^2 + x^5 - 2) |1,0
If a polynomial; use the power rule: #(n^x+1 / x+1)
Integral 1,0 3(4x+x^4)(10x^2 + x^5 - 2)^6 dx
Integral 1,0 3(4x+x^4)(u)^6
dx (du/dx) = 20x + 5x^4 dx
du/(20+5x^4) = (20x+5x^4) dx / 20x + 5x^4
dx = du / 20x+5x^4
Integral 1,0 3(4x+x^4) u^6 du/20x+5x^4
Multiply 1/5 and 5
1/5 Integral 1,0 (5)(3)(4x-x^4)u^6 du/20x+5x^4
3/5 Integral 1,0 (20x-5x^4)u^6 / 20x-5x^4 du
3/5 Integral 1,0 u^6 du
3/5 Integral 1,0 (u^7 / 7) du
Using Power Rule
3/5 (u^7 / 7)
=3/35 (10x^2 + x^5 - 2)^7 |1,0
=3/35 (10(1)^2 + (1)^5 - 2)^7
=409,979.7478
Integral pi/4, 0 8cos(2t) / square root 9-5sin(2t)
Find the U-Sub
u=9-5sin(2t)
du/dt
Integral 1/u^1/2
Integral u^-1/2 du
u= 9-5sin(2t)
du= 9-5sin(2t)
du/dt= -5cos(2t)
Integral pi/4, 0 8cos(2t) / (square root u) dt
Chain Rule
dt (du/dt) = -5cos(2t)(2) dt
dt=du/-10cos(2t)
du/-10cos(2t) = -10cos(2t) / -10cos(2t) dt
Integral pi/4, 0 8cos(2t)/square root u (du/-10cos(2t))
8 Integral pi/4, 0 -10cos(2t)/square root u (du/-10cos(2t))
(-1/10)(8/1) Integral pi/4, 0 -10cos(2t)/square root u (du/-10cos(2t))
-8/10 Integral pi/4, 0 du/square root u
-8/10 Integral pi/4, 0 u^-1/2 du
-8/10 (u^-1/2+1 / -1/2+1) du |pi/4, 0
-8/10 (u^1/2)/(1/2) du |pi/4, u
-8/5 (9-5sin(2t))^1/2 |pi/4, 0
-8/5 (9-5sin(pi/4))^1/2
-8/5 (9-5sin(0))^1/2
=1.059...
Integral 4,1 square root w(e)^1-square root w^3 dw
u=1-square root 1-square root w^3
du=1-square root w^3
dw(du/dw) = -3/2(w^1/2) dw
du/-w = -3/2(w^1/2) dw / -3/2w^1/2
dw = du / -3/2 w^1/2
Integral 4,1 square root w(e)^u du/(-3/2 (w^1/2))
Integral 4,1 square root w(e)^u du(-3/2 (square root w))
-2/3 Integral 4,1 e^u du/(-3/2)
-2/3 Integral 4,1 e^u du
-2/3 (e^u) |4,1
-2/3 e^1-square root w^3 |4,1
(-2/3 e^1-square root 4^3) - (-2/3 e^1-square root 1^3)
=0.66...