Here's a solution I came up with that involves no libraries or packages, just loops and conditionals (accounts for leap years):

def isLeapYear(years):
  if years % 4 == 0:
    if years % 100 == 0:
      if years % 400 == 0:
        return True
      else:
        return False
    else:
      return True
  else:
    return False

monthDays = [31,28,31,30,31,30,31,31,30,31,30,31]
sum = 0
sumDays = []
for i in monthDays:
  sumDays.append(365 - sum)
  sum += i

timeInp = input("Please enter your birthdate in the format dd/mm/yyyy\n")
timeInp = timeInp.split("/")
days = int(timeInp[0])
months = int(timeInp[1])
years = int(timeInp[2])
totDays = 10000

if totDays > 366:
  if isLeapYear(years):
    if months == 1 or months == 2:
      totDays -= (sumDays[months - 1] + 1 - days) + 1
    else:
      totDays -= (sumDays[months - 1] - days) + 1
  else:
    totDays -= (sumDays[months - 1] - days) + 1
  
  months = 1
  days = 1
  years += 1

while totDays > 366:
  if isLeapYear(years):
    totDays -= 366
  else:
    totDays -= 365
  years += 1

i = 0
while totDays != 0:
  if isLeapYear(years):
    monthDays[1] = 29
  else:
    monthDays[1] = 28
    
  if totDays >= monthDays[i]:
    months += 1
    totDays -= monthDays[i]
  elif totDays == monthDays[i]:
    months += 1
    totDays = 0
  else:
    days += totDays 
    if days % (monthDays[i] + 1)!= days:
      days %= monthDays[i] + 1
      months += 1
    totDays = 0

  if months == 13:
    months = 1
    years += 1

  i += 1
  if i == 12:
    i = 0

print(str(days) + "/" + str(months) + "/" + str(years))

As the name suggests, isLeapYear() takes in a parameter years, and returns a boolean value.

Our first step to this problem, to make it easier, is to just first "translate" our date to the next year. This makes our future calculations easier. To do this, we can define an array sumDays that stores the amount of days each month takes to finish the year (go to new years). Then, we subtract this amount from totDays, account for leap years, and update our variables.

Next, is the easy part, just skipping forward by the years while we have enough days for a complete year.

Once we can not add another full year, we just go month by month until we run out of days.

I hope this helped! Please let me know if you need any further details or clarification (or if I made a mistake) :)

Sample Test Cases:

Input #1:

19/05/2008

Output #1:

5/10/2035

Input #2:

05/05/2020

Output #2:

21/9/2047

Input #3:

29/02/2020

Output #3:

17/7/2047

I checked most of my solutions with this website: https://www.countcalculate.com/calendar/birthday-in-days/result

If you import library datetime

import datetime
your_date = "01/05/2000"
(day, month, years) = your_date.split("/")
date = datetime.date(int(years), int(month), int(day))
date_10000 = date+datetime.timedelta(days=10000)
print(date_10000)

No library script

your_date = "20/05/2000"
(day, month, year) = your_date.split("/")
days = 10000
year = int(year)
month = int(month)
day = int(day)
end=False
#m1,m3,m5,m7,m8,m10,m12=31
#m2=28
#m4,m6,m9,m11=30
m=[31,28,31,30,31,30,31,31,30,31,30,31]
while end!=True:
    if(((year % 400 == 0) or  (year % 100 != 0) and  (year % 4 == 0)) and(days-366>=0)):   
        days-=366
        year+=1
    elif(((year % 400 != 0) or  (year % 100 != 0) and  (year % 4 != 0)) and(days-366>=0)):
        days-=365
        year+=1
    else:
        end=True
end=False
if(((year % 400 == 0) or  (year % 100 != 0) and  (year % 4 == 0))):   
    m[1]=29
else:
    m[1]=28
while end!=True:
    if(days-m[month]>=0):
        days-=m[month]
        if(month+1!=12):
            month+=1
        else:
            year+=1
            if(((year % 400 == 0) or  (year % 100 != 0) and  (year % 4 == 0))):   
                m[1]=29
            else:
                m[1]=28
            month=0
    else:
        end=True

if(day+days>m[month]):
    day=day+days-m[month]+1
    if(month+1!=12):
        month+=1
    else:
        year+=1
        if(((year % 400 == 0) or  (year % 100 != 0) and  (year % 4 == 0))):   
            m[1]=29
        else:
            m[1]=28
        month=0
else:
    day=day+days
print(day,"/",month,"/",year)

I have updated my code for the leap year and month dates. Here is the code that I'm using:

n = input("Enter your DOB:(dd/mm/yyyy)")
d,m,y = n.split('/') #Splitting the DOB
d,m,y = int(d), int(m), int(y)
def if_leap(year): # Checking for leap year.
    if year % 4 != 0:
        return False
    elif year % 100 == 0 and year % 400 != 0:
        return False
    else:
        return True


target = 10000
while target > 364: # getting no.of years
    if if_leap(y):
        target -= 366
        y += 1
    else:
        target -= 365
        y += 1

while target > 27: # getting no. of months
    if m == 2 :
        if if_leap(y):
            target -= 29
            m += 1
            if m >= 12: # Resetting the month to 1 if it's value is greater than 12
                y += 1
                m -= 12
        else:
            target -= 28
            m += 1
            if m >= 12:
                y += 1
                m -= 12
    elif m in [1, 3, 5, 7, 8, 10, 12]:
        target -= 31
        m += 1
        if m >= 12:
            y += 1
            m -= 12
    elif m in [4, 6, 9, 11]:
        target -= 30
        m += 1
        if m >= 12:
            y += 1
            m -= 12
            
d = d + target # getting the no. of days
if d > 27:
    if m == 2:
        if if_leap(y):
            d -= 29
            m += 1
        else:
            d -= 28
            m += 1
    elif m in [1, 3, 5, 7, 8, 10, 12]:
        d -= 31
        m += 1
    else:
        d -= 30
        m += 1

print(f"The 10000th date will be {d}/{m}/{y}") 

Output:

Enter your DOB:(dd/mm/yyyy): 06/01/2006
The 10000th date will be 24/5/2033

P.S: I am getting some slightly different outputs when checking with that website. Can anyone figure out the bug/mistake in the code? It'll be really helpful. For eg. for the date 08/12/2004, it should be 25/4/2032 but my output is showing 24/4/2032.